Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Power operations in the Stolz–Teichner program

Tobias Barthel, Daniel Berwick-Evans and Nathaniel Stapleton

Geometry & Topology 26 (2022) 1773–1848
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.

Keywords
elliptic cohomology, supersymmetric field theories, equivariant K-theory, power operations, Stolz–Teichner program
Mathematical Subject Classification
Primary: 55N34, 81T60, 55S25
References
Publication
Received: 2 July 2020
Revised: 26 May 2021
Accepted: 27 June 2021
Published: 28 October 2022
Proposed: Mark Behrens
Seconded: Marc Levine, Stefan Schwede
Authors
Tobias Barthel
Max Planck Institute for Mathematics
Bonn
Germany
Daniel Berwick-Evans
Department of Mathematics
University of Illinois at Urbana–Champaign
Urbana, IL
United States
Nathaniel Stapleton
Department of Mathematics
University of Kentucky
Lexington, KY
United States