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AuthorJohannson, Klaus. author
TitleTopology and Combinatorics of 3-Manifolds [electronic resource] / by Klaus Johannson
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1995
Connect tohttp://dx.doi.org/10.1007/BFb0074005
Descript XVIII, 450 p. online resource

SUMMARY

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


CONTENT

Handlebodies -- Relative handlebodies -- Generalized one-relator 3-manifolds -- N-relaton 3-manifolds -- The space of heegaard graphs


Mathematics Group theory Algebraic topology Manifolds (Mathematics) Complex manifolds Mathematics Algebraic Topology Manifolds and Cell Complexes (incl. Diff.Topology) Group Theory and Generalizations



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