Geometry & Topology, Vol. 5 (2001) Paper no. 3, pages 75--108.

Calculus of clovers and finite type invariants of 3-manifolds

Stavros Garoufalidis, Mikhail Goussarov, Michael Polyak

Abstract. 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

AMS subject classification. Primary: 57N10, 57M27. Secondary: 57M25.

DOI: 10.2140/gt.2001.5.75

E-print: arXiv:math.GT/0005192

Submitted to GT on 19 October 2000. Paper accepted 28 January 2001. Paper published 10 February 2001.

Notes on file formats

Stavros Garoufalidis, Mikhail Goussarov, Michael Polyak

SG: School of Mathematics, Georgia Institute of Technology
Atlanta, GA 30332-0160 USA

MP: School of Mathematics, Tel-Aviv University
69978 Tel-Aviv, Israel


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