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2008 The Jacobi orientation and the two-variable elliptic genus
Matthew Ando, Christopher P French, Nora Ganter
Algebr. Geom. Topol. 8(1): 493-539 (2008). DOI: 10.2140/agt.2008.8.493

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) 595-687] and Hopkins [Proceedings of the ICM 1-2 (1995) 554-565] 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.

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Matthew Ando. Christopher P French. Nora Ganter. "The Jacobi orientation and the two-variable elliptic genus." Algebr. Geom. Topol. 8 (1) 493 - 539, 2008. https://doi.org/10.2140/agt.2008.8.493

Information

Received: 16 June 2006; Revised: 8 November 2007; Accepted: 13 November 2007; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1165.55002
MathSciNet: MR2443236
Digital Object Identifier: 10.2140/agt.2008.8.493

Subjects:
Primary: 55N34

Rights: Copyright © 2008 Mathematical Sciences Publishers

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