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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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On the rigidity theorem for elliptic genera
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by Anand Dessai and Rainer Jung PDF
Trans. Amer. Math. Soc. 350 (1998), 4195-4220 Request permission

Abstract:

We give a detailed proof of the rigidity theorem for elliptic genera. Using the Lefschetz fixed point formula we carefully analyze the relation between the characteristic power series defining the elliptic genera and the equivariant elliptic genera. We show that equivariant elliptic genera converge to Jacobi functions which are holomorphic. This implies the rigidity of elliptic genera. Our approach can be easily modified to give a proof of the rigidity theorem for the elliptic genera of level $N$.
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Additional Information
  • Anand Dessai
  • Affiliation: Department of Mathematics University of Mainz 55099 Mainz Germany
  • Address at time of publication: Department of Mathematics University of Augsburg 86135 Augsburg Germany
  • MR Author ID: 630872
  • Email: dessai@mathpool.Uni-Augsburg.DE
  • Rainer Jung
  • Affiliation: Mathematisches Forschungsinstitut Oberwolfach Lorenzenhof 77709 Oberwolfach Germany
  • Email: jung@MFO.DE
  • Received by editor(s): January 7, 1997
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 4195-4220
  • MSC (1991): Primary 58G10, 19L47, 11F03; Secondary 57S15, 13N10
  • DOI: https://doi.org/10.1090/S0002-9947-98-02321-6
  • MathSciNet review: 1608301