Gems, Computers And Attractors For 3-manifolds
| By: | Sostenes Lins |
| Publisher: | World Scientific Publishing |
| Print ISBN: | 9789810219079 |
| eText ISBN: | 9789812796196 |
| Edition: | 0 |
| Format: | Page Fidelity |
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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.