Topology and Combinatorics of 3-Manifolds

Klaus Johannson (auth.)3540590633, 9783540590637, 0387590633

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

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Table of contents :
Handlebodies….Pages 1-36
Relative handlebodies….Pages 37-146
Generalized one-relator 3-manifolds….Pages 147-245
N-relaton 3-manifolds….Pages 246-282
The space of heegaard graphs….Pages 283-426