Gems, computers, and attractors for 3-manifolds
著者
書誌事項
Gems, computers, and attractors for 3-manifolds
（Series on knots and everything, vol. 5）
World Scientific, c1995
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内容説明・目次
内容説明
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.
目次
- Part 1 Basic theory: E-graphs - special cell-decomposition of 2-manifolds
- crystallizations - the Ferri-Gagliardi moves
- diagrams of E-graphs and Ferri's switching lemma. Part 2 Generating surgery moves: quadricolours, hinges, commuters
- relations among the generating moves
- connections with Lickorish's construction. Part 3 Invariants: the fundamental and the homology groups
- the vertex group ... is there something new here?
- linking invariants. Part 4 Classes of 3-gems: the "planar" class and lens spaces
- gists - special symmetries on 3-manifolds. Part 5 Theory for a catalogue of 3-gems: shortcuts for inserting the 4th colour
- the TS-moves and the U-move. Appendices: all 3-gems up to 28 vertices. (Part Contents).
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