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

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

References

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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

Volume 3, issue 2 (2003)

Gwénaël Massuyeau