Mathematics – Algebraic Topology
Scientific paper
2002-01-10
Geom. Topol. 7 (2003) 91-153
Mathematics
Algebraic Topology
Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper3.abs.html
Scientific paper
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.
Ando Matthew
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