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Topology and Combinatorics of 3-Manifolds

  • Authors
  • Klaus┬áJohannson

Part of the Lecture Notes in Mathematics book series (LNM, volume 1599)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Klaus Johannson
    Pages 1-36
  3. Klaus Johannson
    Pages 37-146
  4. Klaus Johannson
    Pages 147-245
  5. Klaus Johannson
    Pages 246-282
  6. Klaus Johannson
    Pages 283-426
  7. Back Matter
    Pages 427-446

About this book

Introduction

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

Keywords

3-manifolds Fundamental group Heegard surfaces graphs homotopy manifold triangulations

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0074005
  • Copyright Information Springer-Verlag Berlin Heidelberg 1995
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-59063-7
  • Online ISBN 978-3-540-49181-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site