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arXiv · 1908.02868

A de Rham model for complex analytic equivariant elliptic cohomology

Daniel Berwick-Evans·Arnav Tripathy
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Abstract

We construct a cocycle model for complex analytic equivariant elliptic cohomology that refines Grojnowski's theory when the group is connected and Devoto's when the group is finite. We then construct Mathai--Quillen type cocycles for equivariant elliptic Euler and Thom classes, explaining how these are related to positive energy representations of loop groups. Finally, we show that these classes give a unique equivariant refinement of Hopkins' "theorem of the cube" construction of the ${\rm MString}$-orientation of elliptic cohomology.

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BibTeXRIS

Daniel Berwick-Evans, Arnav Tripathy. 2019-08-07. A de Rham model for complex analytic equivariant elliptic cohomology. https://arxiv.org/abs/1908.02868

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