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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the rigidity theorem for elliptic genera


Authors: Anand Dessai and Rainer Jung
Journal: Trans. Amer. Math. Soc. 350 (1998), 4195-4220
MSC (1991): Primary 58G10, 19L47, 11F03; Secondary 57S15, 13N10
MathSciNet review: 1608301
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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
Email: dessai@mathpool.Uni-Augsburg.DE

Rainer Jung
Affiliation: Mathematisches Forschungsinstitut Oberwolfach Lorenzenhof 77709 Oberwolfach Germany
Email: jung@MFO.DE

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02321-6
PII: S 0002-9947(98)02321-6
Keywords: Rigidity theorem, elliptic genera, index theory, Jacobi functions
Received by editor(s): January 7, 1997
Article copyright: © Copyright 1998 American Mathematical Society