Linking forms, reciprocity for Gauss sums and invariants of 3-manifolds

Deloup, Florian

doi:10.1090/S0002-9947-99-02304-1

Linking forms, reciprocity for Gauss sums and invariants of 3-manifolds
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by Florian Deloup

Trans. Amer. Math. Soc. 351 (1999), 1895-1918

DOI: https://doi.org/10.1090/S0002-9947-99-02304-1

Published electronically: January 27, 1999

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Abstract:

We study invariants of $3$-manifolds derived from finite abelian groups equipped with quadratic forms. These invariants arise in Turaev’s theory of modular categories and generalize those of H. Murakami, T. Ohtsuki and M. Okada. The crucial algebraic tool is a new reciprocity formula for Gauss sums, generalizing classical formulas of Cauchy, Kronecker, Krazer and Siegel. We use this reciprocity formula to give an explicit formula for the invariants and to generalize them to higher dimensions.

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