@article{a4b61d67209c42da87eb50a02fa8ec6a,
title = "A de Rham model for complex analytic equivariant elliptic cohomology",
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 complex analytic equivariant refinement of Hopkins' “theorem of the cube” construction of the MString-orientation of elliptic cohomology.",
keywords = "Elliptic cohomology, Equivariant de Rham",
author = "Daniel Berwick-Evans and Arnav Tripathy",
note = "Funding Information: Acknowledgments. Ian Grojnowski's vision for deploying equivariant elliptic cohomology to study representation-theoretic problems has been a constant source of inspiration throughout the duration of this project. A tremendous amount of elliptic cohomology was also developed in notes of Mike Hopkins, to whom we owe a great intellectual debt. We also wish to thank Matt Ando, Nora Ganter, Tom Nevins, Andrei Okounkov, and Charles Rezk for stimulating conversations, Kiran Luecke for comments on an earlier draft, and anonymous referees whose comments helped improve the exposition. Finally, A.T. acknowledges the support of MSRI and the NSF through grants 1705008 and 1440140 . Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",
year = "2021",
month = mar,
day = "26",
doi = "10.1016/j.aim.2021.107575",
language = "English (US)",
volume = "380",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
}