Equivariant elliptic cohomology and twisted equivariant k-theory
Menon, Dileep D.
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https://hdl.handle.net/2142/105744
Description
Title
Equivariant elliptic cohomology and twisted equivariant k-theory
Author(s)
Menon, Dileep D.
Issue Date
2019-05-28
Director of Research (if dissertation) or Advisor (if thesis)
Ando, Matthew
Doctoral Committee Chair(s)
Rezk, Charles
Committee Member(s)
Nevins, Thomas
Berwick-Evans, Daniel
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Elliptic Cohomology, K-Theory, Loop Groups
Abstract
Equivariant elliptic cohomology and twisted equivariant K-theory are both related to the representations of loop groups. After making these relationships precise, we propose a map from twisted equivariant elliptic cohomology to twisted K-theory of the inertia stack using equivariant de Rham models. This proposal agrees with the Freed-Hopkins-Teleman q = 1 map from characters of representations of loop groups to distributions associated to twisted equivariant K-theory classes.
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