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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Cohomology rings, Rochlin function, linking pairing and the Goussarov–Habiro theory of three-manifolds

Gwénaël Massuyeau

Algebraic & Geometric Topology 3 (2003) 1139–1166

arXiv: math.GT/0307396

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
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57R15
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Publication
Received: 1 September 2003
Revised: 9 November 2003
Published: 17 November 2003
Authors
Gwénaël Massuyeau
Institute of Mathematics of the Romanian Academy
P.O. Box 1-764
014700 Bucharest
Romania