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Topology and Combinatorics of 3-Manifolds

  • Book
  • © 1995

Overview

Authors:
  1. Klaus Johannson
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1599)

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About this book

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 (5 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Handlebodies

    • Klaus Johannson
    Pages 1-36

  3. Relative handlebodies

    • Klaus Johannson
    Pages 37-146

  4. Generalized one-relator 3-manifolds

    • Klaus Johannson
    Pages 147-245

  5. N-relaton 3-manifolds

    • Klaus Johannson
    Pages 246-282

  6. The space of heegaard graphs

    • Klaus Johannson
    Pages 283-426

  7. Back Matter

    Pages 427-446
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