Topology and Combinatorics of 3-Manifolds

By Klaus Johannson

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

• Format: Paperback
• Language: English
• ISBN: 3540590633
• ISBN13: 9783540590637
• Release Date: April 1995
• Publisher: Springer
• Length: 450 Pages
• Weight: 1.43 lbs.
• Dimensions: 0.9" x 6.1" x 9.2"