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Calculus of clovers and
finite type invariants of 3–manifolds
Stavros Garoufalidis, Mikhail Goussarov and Michael Polyak |
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Geometry & Topology 5 (2001) 75–108
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DOI: 10.2140/gt.2001.5.75
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arXiv: math.GT/0005192 |
Abstract |
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A clover is a framed trivalent graph with some additional structure, embedded in a 3–manifold. We define surgery on clovers, generalizing surgery on Y–graphs used earlier by the second author to define a new theory of finite-type invariants of 3–manifolds. We give a systematic exposition of a topological calculus of clovers and use it to deduce some important results about the corresponding theory of finite type invariants. In particular, we give a description of the weight systems in terms of uni-trivalent graphs modulo the AS and IHX relations, reminiscent of the similar results for links. We then compare several definitions of finite type invariants of homology spheres (based on surgery on Y–graphs, blinks, algebraically split links, and boundary links) and prove in a self-contained way their equivalence. |
Keywords
3–manifolds, Y–graphs, finite type invariants, clovers
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Mathematical Subject Classification 2000
Primary: 57N10, 57M27
Secondary: 57M25
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References |
Forward citations |
Publication
Received: 19 October 2000
Accepted: 28 January 2001
Published: 10 February 2001
Proposed: Robion Kirby
Seconded: Joan Birman, Cameron Gordon
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Authors |
| Stavros Garoufalidis | |
| School of Mathematics Georgia Institute of Technology Atlanta GA 30332-0160 USA |
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| Mikhail Goussarov | |
| Michael Polyak | |
| School of Mathematics Tel-Aviv University 69978 Tel-Aviv Israel |
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