The Jacobi orientation and the two-variable elliptic genus

Details The Jacobi orientation and the two-variable elliptic genus The Jacobi orientation and the two-variable elliptic genus

2006-05-19

arxiv.org/abs/math/0605554v3

Mathematics

Algebraic Topology

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

Scientific paper

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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