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2003 The sigma orientation for analytic circle-equivariant elliptic cohomology
Matthew Ando
Geom. Topol. 7(1): 91-153 (2003). DOI: 10.2140/gt.2003.7.91


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.


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Matthew Ando. "The sigma orientation for analytic circle-equivariant elliptic cohomology." Geom. Topol. 7 (1) 91 - 153, 2003.


Received: 1 February 2002; Revised: 18 October 2003; Accepted: 19 November 2002; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1021.55004
MathSciNet: MR1988282
Digital Object Identifier: 10.2140/gt.2003.7.91

Primary: 55N34
Secondary: 55N22 , 57R91

Keywords: equivariant elliptic cohomolgy , rigidity , Sigma orientation

Rights: Copyright © 2003 Mathematical Sciences Publishers

Vol.7 • No. 1 • 2003
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