Equivariant elliptic cohomology and the 2-loop groupoid

Matthew Spong

Equivariant elliptic cohomology and the 2-loop groupoid

Algebraic Topology 2024-08-06 v2

Authors: Matthew Spong

Abstract

Following an outline of Rezk, we give a construction of complex-analytic $G$ -equivariant elliptic cohomology for an arbitrary compact Lie group $G$ and we prove some of its fundamental properties. The construction is parametrised over the orbit category of the groupoid of principal $G$ -bundles over 2-dimensional tori and generalises Grojnowski's construction of equivariant elliptic cohomology.

Keywords

equivariant elliptic cohomology compact Lie group orbit category principal G-bundles 2-dimensional torus

Cite

@article{arxiv.2405.18505,
  title  = {Equivariant elliptic cohomology and the 2-loop groupoid},
  author = {Matthew Spong},
  journal= {arXiv preprint arXiv:2405.18505},
  year   = {2024}
}

Comments

38 pages. Submitted version. Exposition improved, citations and references added, Section 6.6 added. Theorem C removed due to an error (to be fixed and included in a subsequent paper)

Equivariant elliptic cohomology and the 2-loop groupoid

Abstract

Keywords

Cite

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