Topology and Combinatorics of 3-Manifolds [electronic resource] / by Klaus Johannson.
Material type: TextSeries: Lecture Notes in Mathematics ; 1599Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1995Description: XVIII, 450 p. online resourceContent type:- text
- computer
- online resource
- 9783540491811
- 514.2 23
- QA612-612.8
Handlebodies -- Relative handlebodies -- Generalized one-relator 3-manifolds -- N-relaton 3-manifolds -- The space of heegaard graphs.
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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