Quadratic functions and complex spin structures on three-manifolds

Florian Deloup (1) , Gwenael Massuyeau (2)

1 LEP - Laboratoire Émile Picard
2 LMJL - Laboratoire de Mathématiques Jean Leray

We show how the space of complex spin structures of a closed oriented three-manifold embeds naturally into a space of quadratic functions associated to its linking pairing. Besides, we extend the Goussarov-Habiro theory of finite type invariants to the realm of compact oriented three-manifolds equipped with a complex spin structure. Our main result states that two closed oriented three-manifolds endowed with a complex spin structure are undistinguishable by complex spin invariants of degree zero if, and only if, their associated quadratic functions are isomorphic.

Domaines: Topologie géométrique [math.GT]

Florian Deloup, Gwenael Massuyeau. Quadratic functions and complex spin structures on three-manifolds. Topology, 2005, 44 (3), pp.509-555. ⟨hal-00135061⟩