Power operations in the Stolz–Teichner program

Tobias Barthel, Daniel Berwick-Evans, Nathaniel Stapleton

Research output: Contribution to journalArticlepeer-review

Abstract

The Stolz–Teichner program proposes a deep connection between geometric field theories and certain cohomology theories. We extend this connection by developing a theory of geometric power operations for geometric field theories restricted to closed bordisms. These operations satisfy relations analogous to the ones exhibited by their homotopical counterparts. We also provide computational tools to identify the geometrically defined operations with the usual power operations on complexified equivariant K–theory. Further, we use the geometric approach to construct power operations for complexified equivariant elliptic cohomology.

Original languageEnglish (US)
Pages (from-to)1773-1848
Number of pages76
JournalGeometry and Topology
Volume26
Issue number4
DOIs
StatePublished - 2022

Keywords

  • elliptic cohomology
  • equivariant K-theory
  • power operations
  • Stolz–Teichner program
  • supersymmetric field theories

ASJC Scopus subject areas

  • Geometry and Topology

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