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The Jacobi orientation and the two-variable elliptic genus

Matthew Ando·Christopher P. French·Nora Ganter
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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.

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Matthew Ando, Christopher P. French, Nora Ganter. 2007-11-08. The Jacobi orientation and the two-variable elliptic genus. https://doi.org/10.2140/agt.2008.8.493

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