Geometry & Topology, Vol. 7 (2003)
Paper no. 3, pages 91--153.
The sigma orientation for analytic circle-equivariant elliptic cohomology
Matthew Ando
Abstract.
We construct a canonical Thom isomorphism in Grojnowski's equivariant
elliptic cohomology, for virtual T-oriented T-equivariant spin bundles
with vanishing Borel-equivariant second Chern class, which is natural
under pull-back of vector bundles and exponential under Whitney
sum. It extends in the complex-analytic 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.
Keywords.
Sigma orientation, equivariant elliptic cohomolgy, rigidity
AMS subject classification.
Primary: 55N34.
Secondary: 55N22, 57R91.
DOI: 10.2140/gt.2003.7.91
E-print: arXiv:math.AT/0201092
Submitted to GT on 1 February 2002.
(Revised 18 October 2002.)
Paper accepted 19 November 2002.
Paper published 17 February 2003.
Notes on file formats
Matthew Ando
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana IL 61801, USA
Email: mando@math.uiuc.edu
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