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

Gwenael Massuyeau (1)

1 IMAR - "Simion Stoilow" Institute of Mathematics

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.

Domaines: Topologie géométrique [math.GT]

Gwenael Massuyeau. Cohomology rings, Rochlin function, linking pairing and the Goussarov-Habiro theory of three-manifolds. Algebr. Geom. Topol., 2003, 3, pp.1139-1166. ⟨hal-00135203⟩