Low dimensional topology:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society [u.a.]
2009
|
| Schriftenreihe: | IAS Park City mathematics series
15 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 313-315) |
| Beschreibung: | XII, 315 S. graph. Darst. |
| ISBN: | 082184766X 9780821847664 |
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| 245 | 1 | 0 | |a Low dimensional topology |c Tomasz S. Mrowka ... ed. |
| 264 | 1 | |a Providence, RI |b American Mathematical Society [u.a.] |c 2009 | |
| 300 | |a XII, 315 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a IAS Park City mathematics series |v 15 | |
| 500 | |a Includes bibliographical references (p. 313-315) | ||
| 650 | 4 | |a Dimension theory (Topology) | |
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Datensatz im Suchindex
| _version_ | 1804140697218973696 |
|---|---|
| adam_text | Contents
Preface
xi
Peter S.
Ozsváth
and
Tomasz S. Mrówka
Introduction
χ
1.
The subject
3
2.
The PCMI Graduate Summer School
3
3.
Acknowledgments
5
John Milnor
Fifty Years Ago: Topology of Manifolds in the 50 s and 60 s
7
1.
3-dimensional manifolds
9
2.
Higher dimensions
10
3.
Why are higher dimensions sometimes easier?
14
4.
Questions from the audience
15
5.
Bibliography
18
Cameron Gordon
Dehn
Surgery and 3-Manifolds
21
Introduction
23
Lecture
1. 3-
manifolds and knots
25
1.1.
3-manifolds
25
1.2.
Knots
27
1.3.
Exercises
29
Lecture
2. Dehn
surgery
31
2.1.
Overview
31
2.2.
Framed surgery on knots on surfaces
34
2.3.
Exercises
35
Lecture
3.
Exceptional
Dehn
surgeries
37
3.1.
Exceptional surgeries
37
3.2.
Lens space surgeries
37
3.3. Seifert
fiber space surgeries
38
3.4.
Toroidal surgeries
39
3.5.
Knots in solid tori
39
3.6.
Exercises
41
vi
CONTENTS
Lecture
4.
Rational tangle filling
43
4.1. Dehn
filling
43
4.2.
Tangles
43
4.3.
Tangles with non-simple double branched covers
47
4.4.
Example: the Whitehead link
47
4.5.
Exercises
50
Lecture
5.
Examples of exceptional
Dehn
fillings
51
5.1.
Some examples
51
5.2.
Chain links
54
5.3.
Simplicity of the double branched cover
56
5.4.
Exercises
57
Lecture
6.
Classification of some exceptional fillings
59
6.1.
Some classification theorems
59
6.2. Seifert
fiber spaces
65
6.3.
Methods of proof; non-integral toroidal surgeries
65
Bibliography
69
David
Gabai
Hyperbolic Geometry and 3-Manifold Topology
73
Introduction
75
1.
Topological tameness; examples and foundations
76
2.
Background material for hyperbolic 3-manifolds
79
3.
Shrinkwrapping
82
4.
Proof of Canary s theorem
86
5.
The tameness criterion
88
6.
Proof of the tameness theorem
96
Bibliography
101
John W. Morgan (notes by Max Lipyanskiy)
Ricci
Flow and Thurston s Geometrization Conjecture
105
Introduction iQY
Lecture
1.
Statement of Thurston s geometrization conjecture
109
1.
Prime decomposition
Ю9
2.
Examples of geometric manifolds
109
3.
Thurston geometrization conjecture
Ш
Lecture
2.
Basics of
Ricci
flow
ИЗ
1.
Conjectures on the geometric structure of 3-manifolds
113
2.
Review of the Riemann curvature tensor
114
3.
The
Ricci
flow equation
ца
CONTENTS
vii
4.
Examples: Einstein manifolds,
Ricci solitone,
and gradient shrinking
solitons
115
5.
Maximum principle
116
6.
Consequences of the maximum principle
117
Lecture
3.
Blow-up limits and «-non-collapsed solutions
119
1.
Definition of blow-up limit
119
2.
Criteria for existence of blow-up limits
119
3.
¿-geodesies and reduced volume
120
4.
Non-collapsing
122
5.
Curvature bounds
122
Lecture
4.
Structure of «-solutions and canonical neighborhoods
123
1.
Gradient shrinking solitons
123
2.
Classification of gradient shrinking solitons
124
3.
«-non-collapsed solutions
124
4.
Canonical neighborhoods
124
5.
Existence of canonical neighborhoods for «-solutions
125
6.
Canonical neighborhoods for
Ricci
flows
125
Lecture
5.
Structure of regions of large curvature and surgery
127
1.
Canonical neighborhoods for regions of high curvature
127
2.
Global versions of tubes and caps
127
3.
Global structure of the regions of large curvature
129
4.
The structure at the singular time
129
5.
The surgery process
129
6.
Auxiliary
Ricci
flow to glue in
130
Lecture
6.
Ricci
flow with surgery and finite-time extinction
131
1.
Ricci
flow with surgery
131
2.
Geometrization
132
Bibliography
137
Marta Asaeda
and Mikhail Khovanov
Notes on Link Homology
139
Introduction
141
Lecture
1.
A braid group action on a category of complexes
143
1.
Path rings
143
2.
Zigzag rings An
144
3.
A functor realization of the Temperley-Lieb algebra
145
4.
The homotopy category of complexes
147
5.
Braid group representation
148
Lecture
2.
More on braid group actions
151
1.
Invertibility of
Лј
151
2.
Braid group action on complexes of
projective
modules
F¿
and topology
of plane curves
151
3.
Reduced
Burau
representation
154
viii CONTENTS
Lecture
3.
A Categorification of the Jones polynomial
157
1.
The Jones polynomial
157
2.
Categorification and a bigraded link homology theory
158
3.
Properties and examples
164
Lecture
4.
Flat tangles and bimodules
169
1.
Two-dimensional TQFTs and Frobenius algebras
169
2.
Algebras
Я
171
3.
Flat tangles and their cobordisms
173
Lecture
5.
A homological invariant of tangles and tangle cobordisms
177
1.
An invariant of tangles
177
2.
Tangle cobordisms
179
3.
Equivariant versions and applications
181
Lecture
6.
Categorifications of the HOMFLY-PT polynomial
185
1.
The HOMFLY-PT polynomial and its generalizations
185
2. Hochschild
homology
186
3.
A categorification of the HOMFLY-PT polynomial
189
Bibliography
193
Zoltán Szabó
Lecture Notes on Heegaard
Floer
Homology
197
Introduction.
199
Acknowledgments.
199
1.
Three-manifolds and Heegaard decompositions.
199
1.1.
Basic examples.
199
1.2.
Heegaard decompositions.
200
1.3.
Exercises for Section
1. 202
2.
Heegaard diagrams.
202
2.1.
Handle decompositions.
202
2.2.
Attaching circles.
203
2.3.
Examples.
203
2.4.
Heegaard moves.
204
2.5.
Exercises for Section
2. 205
3.
Morse functions.
205
3.1.
Exercises for Section
3. 207
4.
Symmetric products and generators.
207
4.1.
Heegaard generators.
208
4.2.
Symmetric products.
208
4.3.
Whitney disks.
209
4.4.
An obstruction for Whitney disks.
210
4.5.
More on homotopy classes and shadows.
210
4.6.
Exercises for Section
4. 211
CONTENTS ix
5.
Pointed diagrams.
212
5.1.
Admissible diagrams.
213
5.2.
Two-pointed Heegaard diagrams.
213
5.3.
Chain-complexes for pointed Heegaard diagrams.
213
5.4.
Chain complexes for knots.
214
5.5.
Exercises for Section
5. 214
6.
Holomorphic disks.
214
6.1.
A mod
2
invariant.
215
6.2.
Properties of the Maslov index.
216
6.3.
Exercises for Section
6. 217
7.
A local formula for the Maslov index.
217
7.1.
Exercises for Section
7. 218
8.
The chain complex.
218
8.1.
Exercises for Section
8. 220
9.
Generators and
spin
-с
structures.
221
9.1.
Exercises for Section
9. 222
10.
Further constructions.
222
10.1.
The construction of HF+{Y,s).
222
10.2.
Orientations.
223
10.3.
Knot
Floer homology.
223
10.4.
Computations.
225
11.
Problems.
225
Bibliography
226
John Etnyre
Contact Geometry in Low Dimensional Topology
229
1.
Introduction
231
2.
Contact structures and foliations
233
3.
From foliations to contact structures
242
3.1.
Part
2
of the proof of Theorem
3.1 244
3.2.
Part
1
of the proof of Theorem
3.1 246
4.
Taut foliations and symplectic fillings
253
5.
Symplectic handle attachment and Legendrian surgery
255
6.
Open book decompositions and symplectic caps
258
Bibliography
262
χ
CONTENTS
Ronald Fintushel and Ronald J. Stern
Six Lectures on Four 4-Manifolds
265
Introduction
267
Lecture
1.
How to construct 4-manifolds
269
1.
Algebraic topology
270
2.
Techniques used for the construction of simply connected smooth and
symplectic 4-manifolds
270
3.
Some examples: Horikawa surfaces
271
4.
Complex surfaces
273
5.
More symplectic manifolds
273
Lecture
2.
A user s guide to Seiberg-
Witten
theory
275
1.
The set-up
275
2.
The equations
277
3.
Adjunction Inequality
278
4. Kahler
manifolds
279
5.
Blowup formula
279
6.
Gluing formula
279
7.
Seiberg-
Witten
invariants of elliptic surfaces
280
8.
Nullhomologous tori
280
9.
Seiberg-
Witten
invariants for log transforms
281
Lecture
3.
Knot surgery
283
1.
The knot surgery theorem
283
2.
Proof of knot surgery theorem: the role of nullhomologous tori
284
Lecture
4.
Rational blowdowns
291
1.
Configurations of spheres and associated rational balls
291
2.
Effect on Seiberg-
Witten
invariants
293
3.
Taut configurations
294
Lecture
5.
Manifolds with b+
= 1 297
1.
Seiberg-
Witten
invariants
297
2.
Smooth structures on blow-ups of CP2
299
Lecture
6.
Putting it all together: The geography and botany of 4-manifolds
305
1.
Existence: the geography problem
305
2.
Uniqueness: the botany problem
307
3.
Horikawa surfaces: how to go from one deformation type to another
308
4.
Manifolds with
с
=
9 h
:
a fake
projective
plane
309
5.
Small 4-manifolds
6.
What were the four 4-manifolds?
Bibliography
|
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| genre | (DE-588)1071861417 Konferenzschrift 2008 Park City Utah gnd-content |
| genre_facet | Konferenzschrift 2008 Park City Utah |
| id | DE-604.BV035768766 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:04:06Z |
| institution | BVB |
| isbn | 082184766X 9780821847664 |
| language | English |
| lccn | 2009000616 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018628507 |
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| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XII, 315 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | American Mathematical Society [u.a.] |
| record_format | marc |
| series | IAS Park City mathematics series |
| series2 | IAS Park City mathematics series |
| spelling | Low dimensional topology Tomasz S. Mrowka ... ed. Providence, RI American Mathematical Society [u.a.] 2009 XII, 315 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier IAS Park City mathematics series 15 Includes bibliographical references (p. 313-315) Dimension theory (Topology) Dimensionstheorie (DE-588)4149935-9 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2008 Park City Utah gnd-content Dimensionstheorie (DE-588)4149935-9 s DE-604 Mrowka, Tomasz 1961- Sonstige (DE-588)138618429 oth IAS Park City mathematics series 15 (DE-604)BV010402400 15 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018628507&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Low dimensional topology IAS Park City mathematics series Dimension theory (Topology) Dimensionstheorie (DE-588)4149935-9 gnd |
| subject_GND | (DE-588)4149935-9 (DE-588)1071861417 |
| title | Low dimensional topology |
| title_auth | Low dimensional topology |
| title_exact_search | Low dimensional topology |
| title_full | Low dimensional topology Tomasz S. Mrowka ... ed. |
| title_fullStr | Low dimensional topology Tomasz S. Mrowka ... ed. |
| title_full_unstemmed | Low dimensional topology Tomasz S. Mrowka ... ed. |
| title_short | Low dimensional topology |
| title_sort | low dimensional topology |
| topic | Dimension theory (Topology) Dimensionstheorie (DE-588)4149935-9 gnd |
| topic_facet | Dimension theory (Topology) Dimensionstheorie Konferenzschrift 2008 Park City Utah |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018628507&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010402400 |
| work_keys_str_mv | AT mrowkatomasz lowdimensionaltopology |