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Topology and Combinatorics of 3-Manifolds : Lecture Notes in Mathematics - Klaus Johannson

Topology and Combinatorics of 3-Manifolds

Lecture Notes in Mathematics

Paperback Published: 21st April 1995
ISBN: 9783540590637
Number Of Pages: 450

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This book is a study of combinatorial structures of 3-mani- folds, especially Haken 3-manifolds. Specifically, it is concerned with Heegard graphs in Haken 3-manifolds, i.e., with graphs whose complements have a free fundamental group. These graphs always exist. They fix not only a combinatorial stucture but also a presentation for the fundamental group of the underlying 3-manifold. The starting point of the book is the result that the intersection of Heegard graphs with incompressible surfaces, or hierarchies of such surfaces, is very rigid. A number of finiteness results lead up to a ri- gidity theorem for Heegard graphs. The book is intended for graduate students and researchers in low-dimensional topolo- gy as well as combinatorial theory. It is self-contained and requires only a basic knowledge of the theory of 3-manifolds

Introduction
Standard Graphs and Meridian-Systemsp. 1
The Disc-Complexp. 10
Homeomorphismsp. 14
Pseudo-Anosov Homeomorphismsp. 23
Branching Complexesp. 24
Heegaard-Diagramsp. 37
Surfacesp. 42
Homeomorphismsp. 59
Dualityp. 64
Presentations for Surfacesp. 84
The Seifert Characteristicp. 94
Algorithms for Surfacesp. 110
The Haken Spectrump. 130
Good Pencilsp. 148
The Handle-Addition Lemma (Absolute Form)p. 152
The Handle-Addition Lemma (Relative Form)p. 162
Homotopy and Isotopyp. 184
The Mapping Class Groupp. 212
Incompressibilityp. 217
The Compression-Algorithmp. 221
The Haken Spectrump. 231
An Examplep. 239
The Handle-Addition Lemma (General Case)p. 247
The Unknotting Theoremp. 269
Distances for Heegaard Graphsp. 276
Constructing Heegaard Graphsp. 289
Haken Complexes and Heegaard Complexesp. 310
Short Companions for Haken Graphsp. 333
Invariant Regions for Long Arc-Sequencesp. 359
The Universal Limit for Induced Haken Graphsp. 376
Finiteness for Heegaard Graphsp. 389
Rigidity for Heegaard Graphsp. 401
Reidemeister-Zieschang Problemp. 423
Appendix. Computing Surfacesp. 427
Referencesp. 436
Indexp. 442
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540590637
ISBN-10: 3540590633
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 450
Published: 21st April 1995
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 2.39
Weight (kg): 0.65