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E-grāmata: 4-Manifolds

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(Professor, Michigan State University)
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This book presents the topology of smooth 4-manifolds in an intuitive self-contained way, developed over a number of years by Professor Akbulut. The text is aimed at graduate students and focuses on the teaching and learning of the subject, giving a direct approach to constructions and theorems which are supplemented by exercises to help the reader work through the details not covered in the proofs.

The book contains a hundred colour illustrations to demonstrate the ideas rather than providing long-winded and potentially unclear explanations. Key results have been selected that relate to the material discussed and the author has provided examples of how to analyse them with the techniques developed in earlier chapters.

Recenzijas

This book is about the art of proving theorems about 4-manifolds by mental visualization and direct interaction with their depictions. Its existence is justifed by the need for an updated treatment...and the need to set out a unifed presentation of the tools and knowledge which have proved most useful over the relatively unique research history of its author. * Jonathan D. Williams, MathSciNet *

Preface vii
1 4-manifold handlebodies
1(18)
1.1 Carving
4(2)
1.2 Sliding handles
6(2)
1.3 Canceling handles
8(2)
1.4 Carving ribbons
10(4)
1.5 Non-orientable handles
14(2)
1.6 Algebraic topology
16(3)
2 Building low-dimensional manifolds
19(18)
2.1 Plumbing
21(1)
2.2 Self plumbing
22(1)
2.3 Some useful diffeomorphisms
23(1)
2.4 Examples
24(5)
2.5 Constructing diffeomorphisms by carving
29(3)
2.6 Shake slice knots
32(1)
2.7 Some classical invariants
33(4)
3 Gluing 4-manifolds along their boundaries
37(6)
3.1 Constructing --M ƒ N by the upside down method
37(2)
3.2 Constructing --M ƒ N and M(ƒ) by the cylinder method (roping)
39(3)
3.3 Codimension zero surgery M → M1
42(1)
4 Bundles
43(12)
4.1 T4 = T2 × T2
43(2)
4.2 Cacime surface
45(7)
4.3 General surface bundles over surfaces
52(1)
4.4 Circle bundles over 3-manifolds
52(1)
4.5 3-manifold bundles over the circle
53(2)
5 3-manifolds
55(9)
5.1 Dehn surgery
56(1)
5.2 From framed links to Heegaard diagrams
57(2)
5.3 Gluing knot complements
59(2)
5.4 Carving 3-manifolds
61(1)
5.5 Rohlin invariant
62(2)
6 Operations
64(14)
6.1 Gluck twisting
64(3)
6.2 Blowing down ribbons
67(1)
6.3 Logarithmic transform
68(1)
6.4 Luttinger surgery
69(2)
6.5 Knot surgery
71(3)
6.6 Rational blowdowns
74(4)
7 Lefschetz fibrations
78(17)
7.1 Elliptic surface E(n)
80(1)
7.2 Dolgachev surfaces
81(3)
7.3 PALFs
84(3)
7.4 ALFs
87(5)
7.5 BLFs
92(3)
8 Symplectic manifolds
95(17)
8.1 Contact manifolds
96(2)
8.2 Stein manifolds
98(1)
8.3 Eliashberg's characterization of Stein
99(2)
8.4 Convex decomposition of 4-manifolds
101(2)
8.5 M4 = |BLF|
103(3)
8.6 Stein = |PALF|
106(1)
8.7 Imbedding Stein to symplectic via PALF
107(2)
8.8 Symplectic fillings
109(3)
9 Exotic 4-manifolds
112(11)
9.1 Constructing small exotic manifolds
112(4)
9.2 Iterated O-Whitehead doubles are non-slice
116(3)
9.3 A solution of a conjecture of Zeeman
119(1)
9.4 An exotic R4
119(1)
9.5 An exotic non-orientable closed manifold
120(3)
10 Cork decomposition
123(15)
10.1 Corks
125(5)
10.2 Anticorks
130(2)
10.3 Knotting corks
132(1)
10.4 Plugs
133(5)
11 Covering spaces
138(12)
11.1 Handlebody of coverings
138(3)
11.2 Handlebody of branched coverings
141(6)
11.3 Branched covers along ribbon surfaces
147(3)
12 Complex surfaces
150(13)
12.1 Milnor fibers of isolated singularities
150(3)
12.2 Hypersurfaces that are branched covers of CP2
153(2)
12.3 Handlebody descriptions of Vd
155(3)
12.4 Σ(a, b, c)
158(5)
13 Seiberg--Witten invariants
163(43)
13.1 Representations
164(2)
13.2 Action of Λ(X) on W±
166(5)
13.3 Dirac operator
171(2)
13.4 A special calculation
173(1)
13.5 Seiberg--Witten invariants
174(7)
13.6 S--W when b+2(X) = 1
181(1)
13.7 Blowup formula
182(1)
13.8 S--W for torus surgeries
182(1)
13.9 S--W for manifolds with T3 boundary
183(2)
13.10 S--W for logarithmic transforms
185(1)
13.11 S--W for knot surgery XK
186(3)
13.12 S--W for S1 × Y3
189(2)
13.13 Moduli space near the reducible solution
191(2)
13.14 Almost complex and symplectic structures
193(7)
13.15 Antiholomorphic quotients
200(1)
13.16 S--W equations on R × Y3
201(1)
13.17 Adjunction inequality
202(4)
14 Some applications
206(39)
14.1 10/8 theorem
206(4)
14.2 Cappell--Shaneson homotopy spheres
210(9)
14.3 Flexible contractible 4-manifolds
219(4)
14.4 Some small closed exotic manifolds
223(22)
14.4.1 An exotic CP2#3CP2
223(11)
14.4.2 An exotic CP2#2CP2
234(9)
14.4.3 Fintushel--Stern reverse engineering
243(2)
References 245(16)
Index 261
Selman Akbulut is a Turkish mathematician and a Professor at Michigan State University. His research is in topology and he has specifically worked on handlebody theory, low-dimensional manifolds, symplectic topology and G2 manifolds with success in developing 4-dimensional handlebody techniques, settling conjectures and solving problems.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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