AGT 3 (2003) Paper 41 (Abstract)

Algebraic and Geometric Topology 3 (2003), paper no. 41, pages 1139-1166.

Cohomology rings, Rochlin function, linking pairing and the Goussarov--Habiro theory of three--manifolds

Gwenael Massuyeau

Abstract. We prove that two closed oriented 3-manifolds have isomorphic quintuplets (homology, space of spin structures, linking pairing, cohomology rings, Rochlin function) if, and only if, they belong to the same class of a certain surgery equivalence relation introduced by Goussarov and Habiro.

Keywords. 3-manifold, surgery equivalence relation, calculus of claspers, spin structure

AMS subject classification. Primary: 57M27. Secondary: 57R15.

DOI: 10.2140/agt.2003.3.1139

E-print: arXiv:math.GT/0307396

Submitted: 1 September 2003. (Revised: 9 November 2003.) Accepted: 9 November2003. Published: 17 November 2003.

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Gwenael Massuyeau
Institute of Mathematics of the Romanian Academy
P.O. Box 1-764, 014700 Bucharest, Romania
Email: gwenael.massuyeau@imar.ro

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