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

Book Title: Topology and Combinatorics of 3-Manifolds
Authors: Klaus Johannson
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0074005
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1995
Softcover ISBN: 978-3-540-59063-7Published: 21 April 1995
eBook ISBN: 978-3-540-49181-1Published: 14 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XVIII, 450
Topics: Algebraic Topology, Manifolds and Cell Complexes (incl. Diff.Topology), Group Theory and Generalizations

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Table of contents (5 chapters)

Front Matter

Handlebodies

Relative handlebodies

Generalized one-relator 3-manifolds

N-relaton 3-manifolds

The space of heegaard graphs

Back Matter

About this book

Keywords

Bibliographic Information

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