The sigma orientation for analytic circle-equivariant elliptic cohomology

Ando, Matthew¹

¹ Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

Geometry & topology, Tome 7 (2003) no. 1, pp. 91-153.

Résumé

We construct a canonical Thom isomorphism in Grojnowski’s equivariant elliptic cohomology, for virtual $\mathbb{T}$–oriented $\mathbb{T}$–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.

Détail

DOI : 10.2140/gt.2003.7.91

Keywords: Sigma orientation, equivariant elliptic cohomolgy, rigidity

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