Topology and Combinatorics of 3-Manifolds / Edition 1

by Klaus Johannson

Overview

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

Product Details

ISBN-13:	9783540590637
Publisher:	Springer Berlin Heidelberg
Publication date:	05/26/1995
Series:	Lecture Notes in Mathematics , #1599
Edition description:	1995
Pages:	450
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

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