The jacobi orientation and the twovariable elliptic genus

Matthew Ando, Christopher P. French, Nora Ganter

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)493-539
Number of pages47
JournalAlgebraic and Geometric Topology
Volume8
Issue number1
DOIs
StatePublished - 2008

Keywords

  • Elliptic genus
  • Equivariant elliptic cohomology
  • Jacobi forms

ASJC Scopus subject areas

  • Geometry and Topology

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