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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Linking forms, reciprocity for Gauss sums and invariants of 3-manifolds
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by Florian Deloup PDF
Trans. Amer. Math. Soc. 351 (1999), 1895-1918 Request permission

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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Additional Information
  • Florian Deloup
  • Affiliation: Institut de Recherche en Mathématiques Avancées 7, rue René Descartes 67084 Strasbourg, France
  • Address at time of publication: Laboratoire de Mathématiques, Emile Picard, Université Paul Sabatier, Toulouse III, 118, route de Narbonne, 31062 Toulouse, France
  • Email: deloup@math.u-strasbg.fr
  • Received by editor(s): April 22, 1997
  • Published electronically: January 27, 1999
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 1895-1918
  • MSC (1991): Primary 11E81, 57N10
  • DOI: https://doi.org/10.1090/S0002-9947-99-02304-1
  • MathSciNet review: 1603898