The Jacobi orientation and the two-variable elliptic genus

Abstract

We explain the relationship between the sigma orientation and Witten genus on the one hand and the two-variable elliptic genus on the other. We show that if E is an elliptic spectrum, then the Theorem of the Cube implies the existence of canonical SU-orientation of the associated spectrum of Jacobi forms. In the case of the elliptic spectrum associated to the Tate curve, this gives the two-variable elliptic genus. We also show that the two-variable genus arises as an instance of the circle-equivariant sigma orientation.

Revised to better exhibit complex orientation of MSU^(CP^\infty_{-infty})

References in corpus (1)

• The sigma orientation for analytic circle-equivariant elliptic cohomology

Cited by in corpus (3)

• Elliptic Genera and Characteristic $q$-Series of Superconformal Field Theory
• The Duistermaat-Heckman formula with application to circle actions and Poincaré $q$-polynomials in twisted equivariant K-theory
• A Relative Lubin-Tate Theorem via Meromorphic Formal Geometry