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The
Jacobi orientation and the two-variable elliptic genus
Matthew Ando, Christopher P French and Nora Ganter |
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Algebraic & Geometric Topology 8 (2008) 493–539
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Abstract |
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Let be an elliptic spectrum with elliptic curve . 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 . As varies we find that the genus is a meromorphic arithmetic Jacobi form. When 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 –equivariant sigma orientation. |
Keywords
elliptic genus, jacobi forms, equivariant elliptic
cohomology
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Mathematical Subject Classification 2000
Primary: 55N34
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References |
Publication
Received: 16 June 2006
Revised: 8 November 2007
Accepted: 13 November 2007
Published: 12 May 2008
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Authors |
| Matthew Ando | |
| Department of Mathematics The University of Illinois at Urbana-Champaign Urbana IL 61801 USA |
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| Christopher P French | |
| Department of Mathematics and
Statistics Grinnell College Grinnell IA 50112 USA |
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| Nora Ganter | |
| Department of Mathematics Colby College Waterville ME 04901 USA |
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