Quadratic functions and complex spin structures on three-manifolds
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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.
41 pages with 10 figures; lightened version (some independent parts of the first version have been moved to other preprints, referenced as math.AC/0301040 and math.GT/0301041 on this server); examples and questions added; exposition improved
41 pages with 10 figures; lightened version (some independent parts of the first version have been moved to other preprints, referenced as math.AC/0301040 and math.GT/0301041 on this server); examples and questions added; exposition improved