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E-grāmata: Basic Algebraic Topology and its Applications

  • Formāts: PDF+DRM
  • Izdošanas datums: 16-Sep-2016
  • Izdevniecība: Springer, India, Private Ltd
  • Valoda: eng
  • ISBN-13: 9788132228431
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Basic Algebraic Topology and its ApplicationsPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 16-Sep-2016
  • Izdevniecība: Springer, India, Private Ltd
  • Valoda: eng
  • ISBN-13: 9788132228431
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This book provides an accessible introduction to algebraic topology, a ?eld at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book o ers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike.

Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.

Recenzijas

Adhikaris work is an excellent resource for any individual seeking to learn more about algebraic topology. By no means will this text feel like an introduction to algebraic topology, but it does offer much for both beginners and experts. the text will be a valuable reference on the bookshelf of any reader with an interest in algebraic topology. Summing Up: Recommended. Upper-division undergraduates and above; researchers and faculty. (A. Misseldine, Choice, Vol. 54 (9), May, 2017)

I am pretty enthusiastic about this book. it shows very good taste on the authors part as far as what hes chosen to do and how hes chosen to do it. Wow! What a nice book. Im glad I have a copy. (Michael Berg, MAA Reviews, maa.org, February, 2017)

This is a comprehensive textbook on algebraic topology. accessible tostudents of all levels of mathematics, so suitable for anyone wanting and needing to learn about algebraic topology. It can also offer a valuable resource for advanced students with a specialized knowledge in other areas who want to pursue their interest in this area. further readings are provided at the end of each of them, which also enables students to study the subject discussed therein in more depth. (Haruo Minami, zbMATH 1354.55001, 2017)

1 Prerequisite Concepts and Notations
1(44)
1.1 Set Theory
1(3)
1.2 Groups and Fundamental Homomorphism Theorem
4(3)
1.3 Group Representations, Free Groups, and Relations
7(4)
1.3.1 Linear Representation of a Group
7(1)
1.3.2 Free Groups and Relations
8(3)
1.3.3 Betti Number and Structure Theorem for Finite Abelian Group
11(1)
1.4 Exact Sequence of Groups
11(2)
1.5 Free Product and Tensor Product of Groups
13(1)
1.5.1 Free Product of Groups
13(1)
1.5.2 Tensor Product of Groups
14(1)
1.6 Torsion Group
14(1)
1.7 Actions of Groups
15(1)
1.8 Modules and Vector Spaces
16(6)
1.8.1 Modules
16(1)
1.8.2 Direct Sum of Modules
17(1)
1.8.3 Tensor Product of Modules
17(3)
1.8.4 Vector Spaces
20(2)
1.9 Euclidean Spaces and Some Standard Notations
22(1)
1.10 Set Topology
22(8)
1.10.1 Topological Spaces: Introductory Concepts
23(2)
1.10.2 Homeomorphic Spaces
25(2)
1.10.3 Metric Spaces
27(1)
1.10.4 Connectedness and Locally Connectedness
28(1)
1.10.5 Compactness and Paracompactness
29(1)
1.10.6 Weak Topology
30(1)
1.11 Partition of Unity and Lebesgue Lemma
30(1)
1.11.1 Lebesgue Lemma and Lebesgue Number
31(1)
1.12 Separation Axioms, Urysohn Lemma, and Tietze Extension Theorem
31(1)
1.13 Identification Maps, Quotient Spaces, and Geometrical Construction
32(5)
1.14 Function Spaces
37(1)
1.15 Manifolds
38(2)
1.16 Exercises
40(3)
1.17 Additional Reading
43(2)
References
43(2)
2 Homotopy Theory: Elementary Basic Concepts
45(62)
2.1 Homotopy: Introductory Concepts and Examples
47(11)
2.1.1 Concept of Homotopy
47(10)
2.1.2 Functorial Representation
57(1)
2.2 Homotopy Equivalence
58(4)
2.3 Homotopy Classes of Maps
62(2)
2.4 H-Groups and H-Cogroups
64(15)
2.4.1 H-Groups and Loop Spaces
65(10)
2.4.2 H-Cogroups and Suspension Spaces
75(4)
2.5 Adjoint Functors
79(4)
2.6 Contractible Spaces
83(5)
2.6.1 Introductory Concepts
83(2)
2.6.2 Infinite-Dimensional Sphere and Comb Space
85(3)
2.7 Retraction and Deformation
88(7)
2.8 NDR and DR Pairs
95(1)
2.9 Homotopy Properties of Infinite Symmetric Product Spaces
96(1)
2.10 Applications
97(3)
2.10.1 Extension Problems
97(2)
2.10.2 Fundamental Theorem of Algebra
99(1)
2.11 Exercises
100(4)
2.12 Additional Reading
104(3)
References
105(2)
3 The Fundamental Groups
107(40)
3.1 Fundamental Groups: Introductory Concepts
108(16)
3.1.1 Basic Motivation
108(1)
3.1.2 Introductory Concepts
109(8)
3.1.3 Functorial Property of π1
117(2)
3.1.4 Some Other Properties of π1
119(5)
3.2 Alternative Definition of Fundamental Groups
124(2)
3.3 Degree Function and the Fundamental Group of the Circle
126(4)
3.4 The Fundamental Group of the Punctured Plane
130(1)
3.5 Fundamental Groups of the Torus
131(1)
3.6 Vector Fields and Fixed Points
132(1)
3.7 Knot and Knot Groups
133(3)
3.8 Applications
136(5)
3.8.1 Fundamental Theorem of Algebra
136(1)
3.8.2 An Alternative Proof of Brouwer Fixed Point Theorem
137(2)
3.8.3 Borsuk--Ulam Theorem
139(1)
3.8.4 Cauchy's Integral Theorem of Complex Analysis
140(1)
3.9 Exercises
141(3)
3.10 Additional Reading
144(3)
References
145(2)
4 Covering Spaces
147(50)
4.1 Covering Spaces: Introductory Concepts and Examples
148(5)
4.1.1 Introductory Concepts
148(3)
4.1.2 Some Interesting Properties of Covering Spaces
151(1)
4.1.3 Covering Spaces of RPn
152(1)
4.2 Computing Fundamental Groups of Figure-Eight and Double Torus
153(2)
4.3 Path Lifting and Homotopy Lifting Properties
155(3)
4.4 Lifting Problems of Arbitrary Continuous Maps
158(3)
4.5 Covering Homomorphisms: Their Classifications and Galois Correspondence
161(9)
4.5.1 Covering Homomorphisms and Deck Transformations
161(2)
4.5.2 Classification of Covering Spaces by Using Group Theory
163(4)
4.5.3 Classification of Covering Spaces and Galois Correspondence
167(3)
4.6 Universal Covering Spaces and Computing π1(RPn)
170(4)
4.6.1 Universal Covering Spaces
170(2)
4.6.2 Computing π1(RPn)
172(2)
4.7 Fibrations and Cofibrations
174(8)
4.7.1 Homotopy Lifting Problems
174(2)
4.7.2 Fibration: Introductory Concepts
176(3)
4.7.3 Cofibration: Introductory Concepts
179(3)
4.8 Hurewicz Theorem for Fibration and Characterization of Fibrations
182(2)
4.9 Homotopy Liftings and Monodromy Theorem
184(2)
4.9.1 Path Liftings and Homotopy Liftings
185(1)
4.9.2 Monodromy Theorem
185(1)
4.10 Applications and Computations
186(6)
4.10.1 Actions of Fundamental Groups
186(1)
4.10.2 Fundamental Groups of Orbit Spaces
187(2)
4.10.3 Fundamental Group of the Real Projective Space RPn
189(1)
4.10.4 The Fundamental Group of Klein's Bottle
189(1)
4.10.5 The Fundamental Groups of Lens Spaces
190(1)
4.10.6 Computing Fundamental Group of Figure-Eight by Graph-theoretic Method
191(1)
4.10.7 Application of Galois Correspondence
191(1)
4.11 Exercises
192(3)
4.12 Additional Reading
195(2)
References
196(1)
5 Fiber Bundles, Vector Bundles and K-Theory
197(52)
5.1 Bundles, Cross Sections, and Examples
198(8)
5.1.1 Bundles
199(1)
5.1.2 Cross Sections
200(1)
5.1.3 Morphisms of Bundles
201(3)
5.1.4 Examples
204(2)
5.2 Fiber Bundles: Introductory Concepts
206(4)
5.3 Hopf and Hurewicz Fiberings
210(3)
5.3.1 Hopf Fibering of Spheres
210(2)
5.3.2 Hurewicz Fibering
212(1)
5.4 G-Bundles and Principal G-Bundles
213(5)
5.5 Homotopy Properties of Numerable Principal G-Bundles
218(2)
5.6 Classifying Spaces: The Milnor Construction
220(3)
5.7 Vector Bundles: Introductory Concepts
223(6)
5.8 Charts and Transition Functions of Bundles
229(4)
5.9 Homotopy Classification of Vector Bundles
233(3)
5.10 K-Theory: Introductory Concepts
236(4)
5.11 Principal G-Bundles for Lie Groups G
240(1)
5.12 Applications
241(1)
5.13 Exercises
241(4)
5.14 Additional Reading
245(4)
References
246(3)
6 Geometry of Simplicial Complexes and Fundamental Groups of Polyhedra
249(24)
6.1 Geometry of Finite Simplicial Complexes
250(3)
6.2 Triangulations and Polyhedra
253(4)
6.3 Simplicial Maps
257(1)
6.4 Barycentric Subdivisions
258(3)
6.5 Simplicial Approximation
261(3)
6.6 Computing Fundamental Groups of Polyhedra
264(1)
6.7 Applications
265(3)
6.7.1 Application to Extension Problem
265(1)
6.7.2 Application to Graph Theory
266(1)
6.7.3 van Kampen Theorem
267(1)
6.8 Exercises
268(2)
6.9 Additional Reading
270(3)
References
271(2)
7 Higher Homotopy Groups
273(32)
7.1 Absolute Homotopy Groups: Introductory Concept
274(3)
7.2 Absolute Homotopy Groups Defined by Hurewicz
277(1)
7.3 Functorial Properties of Absolute Homotopy Groups
278(3)
7.4 The Relative Homotopy Groups: Introductory Concepts
281(1)
7.5 The Boundary Operator and Induced Transformation
282(2)
7.5.1 Boundary Operator
282(1)
7.5.2 Induced Transformations
283(1)
7.6 Functorial Property of the Relative Homotopy Groups
284(1)
7.7 Homotopy Sequence and Its Exactness
285(4)
7.7.1 Homotopy Sequence and Its Exactness
285(2)
7.7.2 Some Consequences of the Exactness of the Homotopy Sequence
287(2)
7.8 Homotopy Sequence of Fibering and Hopf Fibering
289(2)
7.8.1 Homotopy Sequence of Fibering
289(1)
7.8.2 Hopf Fiberings of Spheres
290(1)
7.8.3 Problems of Computing π(Sn)
290(1)
7.9 More on Hopf Maps
291(1)
7.10 Freudenthal Suspension Theorem and Table of π,-(Sn) for 1 ≤ 1, n ≤ 8
292(2)
7.10.1 Freudenthal Suspension Theorem
293(1)
7.10.2 Table of π,(Sn) for 1 ≤ 1, n ≤ 8
294(1)
7.11 Action of π on π
294(1)
7.12 The nth Cohomotopy Sets and Groups
295(2)
7.13 Applications
297(3)
7.14 Exercises
300(2)
7.15 Additional Reading
302(3)
References
303(2)
8 CW-Complexes and Homotopy
305(24)
8.1 Cell-Complexes and CW-Complexes: Introductory Concepts
306(6)
8.1.1 Cell-Complexes
307(1)
8.1.2 CW-Complexes
308(4)
8.1.3 Examples of Spaces Which Are Neither CW-Complexes Nor Homotopy Equivalent to a CW-Complex
312(1)
8.2 Cellular Spaces
312(1)
8.3 Subcomplexes of CW-Complexes
313(1)
8.4 Relative CW-Complexes
314(1)
8.5 Homotopy Properties of CW-Complexes, Whitehead Theorem and Cellular Approximation Theorem
315(4)
8.5.1 Homotopy Properties of CW-Complexes
315(2)
8.5.2 Whitehead Theorem
317(1)
8.5.3 Cellular Approximation Theorem
318(1)
8.6 More on Homotopy Properties of CW-Complexes
319(1)
8.7 Blakers--Massey Theorem and a Generalization of Freudenthal Suspension Theorem
320(1)
8.8 Applications
321(2)
8.9 Exercises
323(2)
8.10 Additional Reading
325(4)
References
326(3)
9 Products in Homotopy Theory
329(18)
9.1 Whitehead Product Between Homotopy Groups of CW-Complexes
329(4)
9.2 Whitehead Products Between Homotopy Groups of H-Spaces
333(2)
9.3 A Generalization of Whitehead Product
335(1)
9.4 Mixed Products in Homotopy Groups
336(2)
9.4.1 Mixed Product in the Homotopy Category of Pointed Topological Spaces
336(1)
9.4.2 Mixed Product Associated with Fibrations
337(1)
9.5 Samelson Products
338(2)
9.5.1 The Samelson Product
338(1)
9.5.2 The Iterated Samleson Product
339(1)
9.6 Some Relations Between Whitehead and Samelson Products
340(1)
9.7 Applications
341(1)
9.7.1 Adams Theorem Using Whitehead Product
341(1)
9.7.2 Homotopical Nilpotence of the Seven Sphere S7
342(1)
9.8 Exercises
342(2)
9.9 Additional Reading
344(3)
References
345(2)
10 Homology and Cohomology Theories
347(60)
10.1 Chain Complexes
349(3)
10.2 Simplicial Homology Theory
352(10)
10.2.1 Construction of Homology Groups of a Simplicial Complex
353(7)
10.2.2 Induced Homomorphism and Functorial Properties of Simplicial Homology
360(1)
10.2.3 Computing Homology Groups of Polyhedra
361(1)
10.3 Relative Simplicial Homology Groups
362(2)
10.4 Exactness of Simplicial Homology Sequences
364(1)
10.5 Simplicial Cohomology Theory: Introductory Concepts
365(2)
10.6 Simplicial Cohomology Ring
367(1)
10.7 Singular Homology
368(6)
10.7.1 Singular Homology Groups
369(3)
10.7.2 Reduced Singular Homology Groups
372(1)
10.7.3 Relative Singular Homology Groups
373(1)
10.8 Eilenberg--Zilber Theorem and Kunneth Formula
374(1)
10.8.1 Eilenberg--Zilber Theorem
374(1)
10.8.2 Kunneth Formula
374(1)
10.9 Singular Cohomology
375(1)
10.10 Relative Cohomology Groups
376(1)
10.11 Hurewicz Homomorphism
377(2)
10.12 Mayer--Vietoris Sequences
379(2)
10.12.1 Mayer--Vietoris Sequences in Singular Homology Theory
379(1)
10.12.2 Mayer--Vietoris Sequences in Simplicial Homology Theory
380(1)
10.13 Computing Homology Groups
381(2)
10.13.1 Homology Groups of a One-Point Space
381(1)
10.13.2 Homology Groups of CW-complexes
382(1)
10.14 Cellular Homology
383(1)
10.15 Cech Homology and Cohomology Groups
384(1)
10.16 Universal Coefficient Theorem for Homology and Cohomology
385(3)
10.16.1 Homology with Arbitrary Coefficient Group
385(2)
10.16.2 Universal Cohomology Theorem for Cohomology
387(1)
10.17 Betti Number and Euler Characteristic
388(4)
10.17.1 Euler Characteristics of Polyhedra
388(2)
10.17.2 Euler Characteristic of Finite Graphs
390(1)
10.17.3 Euler Characteristic of Graded Vector Spaces
390(1)
10.17.4 Euler--Poincare Theorem for Finite CW-complexes
391(1)
10.18 Cup and Cap Products in Cohomology Theory
392(4)
10.18.1 Cup Product
393(2)
10.18.2 Cap Product
395(1)
10.19 Applications
396(2)
10.19.1 Jordan Curve Theorem
396(1)
10.19.2 Homology Groups of of √ αεa Snα
397(1)
10.20 In variance of Dimension
398(1)
10.21 Exercises
399(5)
10.22 Additional Reading
404(3)
References
406(1)
11 Eilenberg--MacLane Spaces
407(12)
11.1 Eilenberg--MacLane Spaces: Introductory Concept
407(2)
11.2 Construction of Eilenberg--MacLane Spaces K(G, n)
409(4)
11.2.1 A Construction of K(G, 1)
409(1)
11.2.2 A Construction of K(G, n) for n < 1
409(1)
11.2.3 Moore Spaces
410(1)
11.2.4 Killing Homotopy Groups
410(1)
11.2.5 Postnikov Tower: Its Existence and Construction
411(2)
11.2.6 Existence Theorem
413(1)
11.3 Applications
413(2)
11.4 Exercises
415(1)
11.5 Additional Reading
416(3)
References
417(2)
12 Eilenberg--Steenrod Axioms for Homology and Cohomology Theories
419(14)
12.1 Eilenberg--Steenrod Axioms for Homology Theory
420(2)
12.2 The Uniqueness Theorem for Homology Theory
422(2)
12.3 Eilenberg--Steenrod Axioms for Cohomology Theory
424(3)
12.4 The Reduced 0-dimensional Homology and Cohomology Groups
427(1)
12.5 Applications
427(2)
12.5.1 Invariance of Homology Groups
428(1)
12.5.2 Invariance of Cohomology Groups
428(1)
12.5.3 Mayer--Vietoris Theorem
428(1)
12.6 Exercises
429(1)
12.7 Additional Reading
430(3)
References
431(2)
13 Consequences of the Eilenberg--Steenrod Axioms
433(12)
13.1 Immediate Consequences
433(7)
13.2 Applications
440(2)
13.2.1 Cofibration and Homology
440(1)
13.2.2 Computing Ordinary Homology Groups of Sn
441(1)
13.3 Exercises
442(1)
13.4 Additional Reading
443(2)
References
443(2)
14 Applications
445(30)
14.1 Degrees of Spherical Maps and Their Applications
445(6)
14.1.1 Degree of a Spherical Map
446(3)
14.1.2 Hopf Classification Theorem
449(1)
14.1.3 The Brouwer Fixed Point Theorem
450(1)
14.2 Continuous Vector Fields
451(2)
14.3 Borsuk-Ulam Theorem with Applications
453(2)
14.3.1 Borsuk--Ulam Theorem
453(1)
14.3.2 Ham Sandwich Theorem
454(1)
14.3.3 Lusternik--Schnirelmann Theorem
455(1)
14.4 The Lefschetz Number and Fixed Point Theorems
455(3)
14.5 Application of Euler Characteristic
458(2)
14.6 Application of Mayer--Vietoris Sequence
460(1)
14.7 Application of van Kampen Theorem
461(1)
14.8 Applications to Algebra
462(1)
14.9 Application of Brown Functor
463(1)
14.10 Applications Beyond Mathematics
464(3)
14.10.1 Application to Physics
464(1)
14.10.2 Application to Sensor Network
465(1)
14.10.3 Application to Chemistry
465(1)
14.10.4 Application to Biology, Medical Science and Biomedical Engineering
466(1)
14.10.5 Application to Economics
466(1)
14.10.6 Application to Computer Science
467(1)
14.11 Exercises
467(4)
14.12 Additional Reading
471(4)
References
472(3)
15 Spectral Homology and Cohomology Theories
475(36)
15.1 Spectrum of Spaces
476(1)
15.2 Spectral Reduced Homology Theory
477(3)
15.3 Spectral Reduced Cohomology Theory
480(1)
15.4 Generalized Homology and Cohomology Theories
481(1)
15.5 The Brown Representability Theorem
481(3)
15.6 A Generalization of Eilenberg--MacLane Spectrum and Construction of Its Associated Generalized Cohomology Theory
484(3)
15.6.1 Construction of a New Ω-Spectrum Δ
484(1)
15.6.2 Construction of the Cohomology Theory Associated with Δ
485(2)
15.7 K-Theory as a Generalized Cohomology Theory
487(1)
15.8 Spectral Unreduced Homology and Cohomology Theories
488(1)
15.9 Cohomology Operations
489(7)
15.9.1 Cohomology Operations of Type (G, n; T, m) and Eilenberg-MacLane Spaces
490(1)
15.9.2 Cohomology Operation Associated with a Spectrum
491(1)
15.9.3 Stable Cohomology Operations
492(1)
15.9.4 A Characterization of the Group {Omk}
493(3)
15.10 Stable Homotopy Theory and Homotopy Groups Associated with a Spectrum
496(3)
15.10.1 Stable Homotopy Groups
496(2)
15.10.2 Homology Groups Associated with a Spectrum
498(1)
15.10.3 Homotopy Groups Associated with a Spectrum
499(1)
15.11 Applications
499(7)
15.11.1 Poincare Duality Theorem
500(2)
15.11.2 Homotopy Type of the Eilenberg--MacLane Space K(G,n)
502(1)
15.11.3 Application of Representability Theorem of Brown
503(1)
15.11.4 More Applications of Spectra
504(1)
15.11.5 Homotopical Description of Singular Cohomology Theory
505(1)
15.12 Exercises
506(2)
15.13 Additional Reading
508(3)
References
509(2)
16 Obstruction Theory
511(22)
16.1 Basic Aim of Obstruction Theory
512(3)
16.1.1 The Extension Problem
513(1)
16.1.2 The Lifting Problem
514(1)
16.1.3 Relative Lifting Problem
514(1)
16.1.4 Cross Section Problem
515(1)
16.2 Notations and Abbreviations
515(1)
16.3 The Obstruction Theory: Basic Concepts
516(7)
16.3.1 The Obstruction Cochains and Cocycles
516(3)
16.3.2 The Deformation and Difference Cochains
519(1)
16.3.3 The Eilenberg Extension Theorem
520(1)
16.3.4 The Obstruction Set for Extension
521(1)
16.3.5 The Homotopy Index
522(1)
16.4 Applications
523(4)
16.4.1 A Link between Cohomolgy and Homotopy with Hopf Theorem
523(1)
16.4.2 Stepwise Extension of A Cross Section
524(2)
16.4.3 Homological Version of Whitehead Theorem
526(1)
16.4.4 Obstruction for Homotopy Between Relative Lifts
526(1)
16.5 Exercises
527(3)
16.6 Additional Reading
530(3)
References
530(3)
17 More Relations Between Homology and Homotopy
533(14)
17.1 Some Similarities and Key Links
534(2)
17.1.1 Some Similarities
534(1)
17.1.2 Hurewicz Homomorphism Theorem: A Key Link
534(2)
17.2 Relative Version of Hurewicz Homomorphism Theorem
536(1)
17.3 Alternative Proof of Homological Version of Whitehead Theorem
537(1)
17.4 Dold--Thom Theorem
538(1)
17.5 The Hopf Invariant and Adams Theorem
539(3)
17.5.1 Hopf Invariant
539(2)
17.5.2 Vector Field Problem and Adams Theorem
541(1)
17.6 Exercises
542(3)
17.7 Additional Reading
545(2)
References
545(2)
18 A Brief History of Algebraic Topology
547(22)
18.1 Poincare and his Conjecture
548(2)
18.2 Early Development of Homotopy Theory
550(4)
18.3 Category Theory and CW-Complexes
554(1)
18.4 Early Development of Homology Theory
555(2)
18.5 Hopf Invariant
557(1)
18.6 Eilenberg and Steenrod Axioms
558(1)
18.7 Fiber Bundle, Vector Bundle, and K-Theory
559(2)
18.8 Eilenberg--MacLane Spaces and Cohomology Operations
561(1)
18.9 Generalized Homology and Cohomology Theories
562(1)
18.10 Ω-Spectrum and Associated Cohomology Theories
563(1)
18.11 Brown Representability Theorem
564(1)
18.12 Obstruction Theory
565(1)
18.13 Additional Reading
566(3)
References
567(2)
Appendix A Topological Groups and Lie Groups 569(12)
Appendix B Categories, Functors and Natural Transformations 581(18)
List of Symbols 599(8)
Author Index 607(2)
Subject Index 609
Mahima Ranjan Adhikari, PhD, is a former professor of Pure Mathematics at the University of Calcutta. His main interest lies in algebra and topology. He has published a number of papers in several international journals including the Proceedings of American Mathematical Society and ve textbooks. Eleven students have already been awarded the PhD degree under his supervision. He is a member of the American Mathematical Society and serves on the editorial board of several journals and research monographs. He was the president of the mathematical science section of the 95th Indian Science Congress, 2008. He has visited several institutions in India, USA, UK, Japan, France, Greece, Sweden, Switzerland, Italy and many other countries on invitation. While visiting E.T.H., Zurich, Switzerland, in 2003, he made an academic interaction with Professor B Eckmann and P J Hilton. He is currently the president of the Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC). He is also the principal investigator of an ongoing project funded by the Government of India. The present book is written based on authors teaching experience of 50 years. He is the joint author ( with Avishek Adhikari) of another Springer book Basic Modern Algebra with Applications, 2014.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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