Circle-equivariant classifying spaces and the rational equivariant sigma genus
Algebraic Topology
2010-07-23 v3
Abstract
The circle-equivariant spectrum MString_C is the equivariant analogue of the cobordism spectrum MU<6> of stably almost complex manifolds with c_1=c_2=0. Given a rational elliptic curve C, the second author has defined a ring T-spectrum EC representing the associated T-equivariant elliptic cohomology. The core of the present paper is the construction, when C is a complex elliptic curve, of a map of ring T-spectra MString_C --> EC which is the rational equivariant analogue of the sigma orientation of Ando-Hopkins-Strickland. We support this by a theory of characteristic classes for calculation, and a conceptual description in terms of algebraic geometry. In particular, we prove a conjecture of the first author.
Cite
@article{arxiv.0705.2687,
title = {Circle-equivariant classifying spaces and the rational equivariant sigma genus},
author = {Matthew Ando and J. P. C. Greenlees},
journal= {arXiv preprint arXiv:0705.2687},
year = {2010}
}