Quadratic functions and complex spin structures on three-manifolds

Florian Deloup; Gwenael Massuyeau

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arXiv · math/0207188

Quadratic functions and complex spin structures on three-manifolds

Florian Deloup·Gwenael Massuyeau

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Abstract

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.

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BibTeX RIS

Florian Deloup, Gwenael Massuyeau. 2004-10-15. Quadratic functions and complex spin structures on three-manifolds. https://arxiv.org/abs/math/0207188

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