Title:
The sigma orientation for analytic circle-equivariant elliptic cohomology
Author:
Matthew Ando
MSC:
55N34 (Primary); 55N22, 57R91 (Secondary)
Arxiv:
math.AT/0201092
Address:
Department of Mathematics
University of Illinois at Urbana-Champaign
E-mail:
mando@math.uiuc.edu
Abstract:
Let T be the circle group. We construct a canonical Thom isomorphism
in T-equivariant analytic elliptic cohomology, for T-oriented virtual
vector bundles bundles whose Borel-equivariant second Stiefel-Whitney
and second Chern classes vanish. The construction is natural under
pull-back of vector bundles and exponential under Whitney sum. It
extends in the rational case the non-equivariant sigma orientation of
Hopkins, Strickland, and the author. The construction relates the
sigma orientation to the representation theory of loop groups and
Looijenga's weighted projective space, and sheds light even on the
non-equivariant case. Rigidity theorems of Witten-Bott-Taubes
including generalizations by Kefeng Liu follow.