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On the rigidity theorem for elliptic genera

Author(s): Anand Dessai; Rainer Jung
Journal: Trans. Amer. Math. Soc. 350 (1998), 4195-4220.
MSC (1991): Primary 58G10, 19L47, 11F03; Secondary 57S15, 13N10
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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: 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
Copyright of article: Copyright 1998, American Mathematical Society

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