The jacobi orientation and the twovariable elliptic genus

Matthew Ando; Christopher P. French; Nora Ganter

doi:10.2140/agt.2008.8.493

The jacobi orientation and the twovariable elliptic genus

Matthew Ando, Christopher P. French, Nora Ganter

Research output: Contribution to journal › Article › peer-review

Abstract

Let E be an elliptic spectrum with elliptic curve C. We show that the sigma orientation of Ando, Hopkins and Strickland [Invent. Math 146 (2001) 595687] and Hopkins [Proceedings of the ICM 12 (1995) 554565] gives rise to a genus of SU -manifolds taking its values in meromorphic functions on C. As C varies we find that the genus is a meromorphic arithmetic Jacobi form. When C is the Tate elliptic curve it specializes to the two variable elliptic genus studied by many. We also show that this two variable genus arises as an instance of the S1-equivariant sigma orientation.

Original language	English (US)
Pages (from-to)	493-539
Number of pages	47
Journal	Algebraic and Geometric Topology
Volume	8
Issue number	1
DOIs	https://doi.org/10.2140/agt.2008.8.493
State	Published - 2008

Keywords

Elliptic genus
Equivariant elliptic cohomology
Jacobi forms

ASJC Scopus subject areas

Geometry and Topology

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The jacobi orientation and the twovariable elliptic genus

Abstract

Keywords

ASJC Scopus subject areas

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