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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 |
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