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) |
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Pages (from-to) | 493-539 |
Number of pages | 47 |
Journal | Algebraic and Geometric Topology |
Volume | 8 |
Issue number | 1 |
DOIs | |
State | Published - 2008 |
Keywords
- Elliptic genus
- Equivariant elliptic cohomology
- Jacobi forms
ASJC Scopus subject areas
- Geometry and Topology