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2022 Power operations in the Stolz–Teichner program
Tobias Barthel, Daniel Berwick-Evans, Nathaniel Stapleton
Geom. Topol. 26(4): 1773-1848 (2022). DOI: 10.2140/gt.2022.26.1773

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.

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Tobias Barthel. Daniel Berwick-Evans. Nathaniel Stapleton. "Power operations in the Stolz–Teichner program." Geom. Topol. 26 (4) 1773 - 1848, 2022. https://doi.org/10.2140/gt.2022.26.1773

Information

Received: 2 July 2020; Revised: 26 May 2021; Accepted: 27 June 2021; Published: 2022
First available in Project Euclid: 11 November 2022

Digital Object Identifier: 10.2140/gt.2022.26.1773

Subjects:
Primary: 55N34 , 55S25 , 81T60

Keywords: elliptic cohomology , equivariant K-theory , power operations , Stolz–Teichner program , supersymmetric field theories

Rights: Copyright © 2022 Mathematical Sciences Publishers

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Vol.26 • No. 4 • 2022
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