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Series on Knots and Everything - Vol. 5

GEMS, COMPUTERS AND ATTRACTORS FOR 3-MANIFOLDS

by Sóstenes Lins (Universidade Federal de Pernambuco, Brazil)

This book is about dealing with 3-manifolds using computers. Its emphasis is on presenting algorithms which are used for solving (in practice) the homeomorphism problem for the smallest of these objects. The key concept is the 3-gem, a special kind of edge-colored graph, which encodes the manifold via a ball complex. Passages between 3-gems and more standard presentations like Heegaard diagrams and surgery descriptions are provided. A catalogue of all closed orientable 3-manifolds induced by 3-gems up to 30 vertices is included. In order to help the classification, various invariants are presented, including the new quantum invariants.


Contents:

  • Introduction
  • Graph-Encoded Manifolds
  • Elements of the Theory of 3-Gems
  • Decomposition Theory: Handles
  • Simplifying Dynamics: The TSup-Algorithm
  • The Generation and Classification of 3-Manifolds
  • Getting Linking Numbers of 3-Manifolds
  • Computing the Quantum Invariants from Blinks
  • Appendices


Readership: Mathematicians.

468pp Pub. date: Sept 1995
ISBN 981-02-1907-5 US$83 / £57


Copyright © 2008 World Scientific Publishing Co. All rights reserved.
Updated on 17 November 2008