The Jacobi orientation and the two-variable elliptic genus
Algebraic Topology
2014-10-01 v3 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.math/0605554,
title = {The Jacobi orientation and the two-variable elliptic genus},
author = {Matthew Ando and Christopher P. French and Nora Ganter},
journal= {arXiv preprint arXiv:math/0605554},
year = {2014}
}
Comments
Revised to better exhibit complex orientation of MSU^(CP^\infty_{-infty})