On the decategorification of some higher actions in Heegaard Floer homology

Manion, Andrew

doi:10.2140/agt.2024.24.1157

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On the decategorification of some higher actions in Heegaard Floer homology

Andrew Manion

Algebraic & Geometric Topology 24 (2024) 1157–1182

DOI: 10.2140/agt.2024.24.1157

Abstract

We decategorify the higher actions on bordered Heegaard Floer strands algebras from recent work of Rouquier and the author, and identify the decategorifications with certain actions on exterior powers of homology groups of surfaces. We also suggest an interpretation for these actions in the language of open-closed TQFT, and we prove a corresponding gluing formula.

Keywords

decategorification, Heegaard Floer, bordered Floer, higher representation, open-closed TQFT

Mathematical Subject Classification

Primary: 57K16

Secondary: 18N25, 57K18

References

Publication

Received: 12 March 2022

Revised: 17 July 2022

Accepted: 10 August 2022

Published: 12 April 2024

Authors

Andrew Manion
Department of Mathematics North Carolina State University Raleigh, NC United States
https://math.sciences.ncsu.edu/people/ajmanion/

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Volume 24, issue 2 (2024)