4-manifolds:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford, United Kingdom
Oxford University Press
2016
|
| Edition: | First edition |
| Series: | Oxford graduate texts in mathematics
25 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | xii, 262 Seiten Illustrationen, Diagramme |
| ISBN: | 9780198784869 0198784864 |
Staff View
MARC
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| 245 | 1 | 0 | |a 4-manifolds |c Selman Akbulut |
| 246 | 1 | 3 | |a Four-manifolds |
| 250 | |a First edition | ||
| 264 | 1 | |a Oxford, United Kingdom |b Oxford University Press |c 2016 | |
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Record in the Search Index
| _version_ | 1804176449918205952 |
|---|---|
| adam_text | Contents
Preface vii
1 4-manifold handlebodies 1
1.1 Carving ............................................................ 4
1.2 Sliding handles..................................................... 6
1.3 Canceling handles................................................... 8
1.4 Carving ribbons ................................................... 10
1.5 Non-orientable handles............................................. 14
1.6 Algebraic topology................................................. 16
2 Building low-dimensional manifolds 19
2.1 Plumbing .......................................................... 21
2.2 Self plumbing...................................................... 22
2.3 Some useful diffeomorphisms........................................ 23
2.4 Examples ........................................................ 24
2.5 Constructing diffeomorphisms by carving............................ 29
2.6 Shake slice knots.................................................. 32
2.7 Some classical invariants ......................................... 33
3 Gluing 4-manifolds along their boundaries 37
3.1 Constructing -M N by the upside down method........................ 37
3.2 Constructing -M N and M(f) by the cylinder method (roping) .... 39
3.3 Codimension zero surgery M ֊ M .................................. 42
4 Bundles 43
4.1 T4 = T2xT2.................................................... 43
4.2 Cacime surface..................................................... 45
4.3 General surface bundles over surfaces.............................. 52
ix
Contents
4.4 Circle bundles over 3-manifolds....................................... 52
4.5 3-manifold bundles over the circle.................................... 53
5 3-manifolds 55
5.1 Dehn surgery.......................................................... 56
5.2 From framed links to Heegaard diagrams................................ 57
5.3 Gluing knot complements............................................... 59
5.4 Carving 3-manifolds................................................... 61
5.5 Rohlin invariant ..................................................... 62
6 Operations 64
6.1 Gluck twisting ....................................................... 64
6.2 Blowing down ribbons.................................................. 67
6.3 Logarithmic transform................................................. 68
6.4 Luttinger surgery..................................................... 69
6.5 Knot surgery.......................................................... 71
6.6 Rational blowdowns.................................................... 74
7 Lefschetz fibrations 78
7.1 Elliptic surface E(n)................................................. 80
7.2 Dolgachev surfaces ................................................... 81
7.3 PALFs................................................................. 84
7.4 ALFs ................................................................. 87
7.5 BLFs ................................................................ 92
8 Symplectic manifolds 95
8.1 Contact manifolds.................................................... 96
8.2 Stein manifolds.................................................... 98
8.3 Eliashberg’s characterization of Stein............................... 99
8.4 Convex decomposition of 4-manifolds..................................101
8.5 M4 = BLF ......................................................... 103
8.6 Stein = PALF ..................................................... 106
8.7 Imbedding Stein to symplectic via PALF...............................107
8.8 Symplectic fillings..................................................109
9 Exotic 4-manifolds 112
9.1 Constructing small exotic manifolds .................................112
9.2 Iterated 0-Whitehead doubles are non-slice............................116
9.3 A solution of a conjecture of Zeeman..................................119
x
Contents
9.4 An exotic R4 ........................................................119
9.5 An exotic non-orientable closed manifold ...........................120
10 Cork decomposition 123
10.1 Corks................................................................125
10.2 Anticorks .......................................................... 130
10.3 Knotting corks.......................................................132
10.4 Plugs................................................................133
11 Covering spaces 138
11.1 Handlebody of coverings .............................................138
11.2 Handlebody of branched coverings ................................... 141
11.3 Branched covers along ribbon surfaces................................147
12 Complex surfaces 150
12.1 Milnor fibers of isolated singularities..............................150
12.2 Hypersurfaces that are branched covers of CP2....................... 153
12.3 Handlebody descriptions of Vd....................................... 155
12.4 E(a,6,c).............................................................158
13 Seiberg—Witten invariants 163
13.1 Representations......................................................164
13.2 Action of A*(AT) on W± .........................................166
13.3 Dirac operator ..................................................... 171
13.4 A special calculation............................................... 173
13.5 Seiberg-Witten invariants........................................... 174
13.6 S-W when 62(A) = 1................................................. 181
13.7 Blowup formula...................................................... 182
13.8 S-W for torus surgeries............................................. 182
13.9 S-W for manifolds with T3 boundary...................................183
13.10 S-W for logarithmic transforms......................................185
13.11 S-W for knot surgery Xk............................................ 18b
13.12 S-W for S 1 x Y3....................................................189
13.13 Moduli space near the reducible solution............................191
13.14 Almost complex and symplectic structures.......................... 193
13.15 Antiholomorphic quotients...........................................200
13.16 S-W equations onRxF3................................................201
13.17 Adjunction inequality...............................................202
xi
Contents
14 Some applications 206
14.1 10/8 theorem......................................................206
14.2 Cappell-Shaneson homotopy spheres.................................210
14.3 Flexible contractible 4-manifolds ................................219
14.4 Some small closed exotic manifolds................................223
14.4.1 An exotic CP2#3CP2.........................................223
14.4.2 An exotic CP2#2CP2.........................................234
14.4.3 Fintushel-Stern reverse engineering........................243
References 245
Index 261
xii
4-Manifold$ 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.
Uniquely, this work contains a hundred color 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
howto analyse them with the techniques developed in earlier chapters.
Selman Akbulut is a Professor at Michigan State University. His research is in topology;
he has worked on topology of real algebraic sets, symplectic and G2 manifolds, and on
low-dimensional manifolds with success in developing 4-dimensional handlebody
techniques, settling conjectures and solving problems.
|
| any_adam_object | 1 |
| author | Akbulut, Selman 1949- |
| author_GND | (DE-588)113177216 |
| author_facet | Akbulut, Selman 1949- |
| author_role | aut |
| author_sort | Akbulut, Selman 1949- |
| author_variant | s a sa |
| building | Verbundindex |
| bvnumber | BV043681972 |
| classification_rvk | SK 370 SK 350 |
| ctrlnum | (OCoLC)953317029 (DE-599)BVBBV043681972 |
| dewey-full | 514.34 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.34 |
| dewey-search | 514.34 |
| dewey-sort | 3514.34 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | First edition |
| format | Book |
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| id | DE-604.BV043681972 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:32:22Z |
| institution | BVB |
| isbn | 9780198784869 0198784864 |
| language | English |
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| physical | xii, 262 Seiten Illustrationen, Diagramme |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Oxford University Press |
| record_format | marc |
| series | Oxford graduate texts in mathematics |
| series2 | Oxford graduate texts in mathematics Oxford mathematics |
| spelling | Akbulut, Selman 1949- Verfasser (DE-588)113177216 aut 4-manifolds Selman Akbulut Four-manifolds First edition Oxford, United Kingdom Oxford University Press 2016 xii, 262 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Oxford graduate texts in mathematics 25 Oxford mathematics Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Dimension 4 (DE-588)4338676-3 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Dimension 4 (DE-588)4338676-3 s DE-604 Oxford graduate texts in mathematics 25 (DE-604)BV011416591 25 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029094833&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029094833&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Akbulut, Selman 1949- 4-manifolds Oxford graduate texts in mathematics Mannigfaltigkeit (DE-588)4037379-4 gnd Dimension 4 (DE-588)4338676-3 gnd |
| subject_GND | (DE-588)4037379-4 (DE-588)4338676-3 |
| title | 4-manifolds |
| title_alt | Four-manifolds |
| title_auth | 4-manifolds |
| title_exact_search | 4-manifolds |
| title_full | 4-manifolds Selman Akbulut |
| title_fullStr | 4-manifolds Selman Akbulut |
| title_full_unstemmed | 4-manifolds Selman Akbulut |
| title_short | 4-manifolds |
| title_sort | 4 manifolds |
| topic | Mannigfaltigkeit (DE-588)4037379-4 gnd Dimension 4 (DE-588)4338676-3 gnd |
| topic_facet | Mannigfaltigkeit Dimension 4 |
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