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On the decategorification of some higher actions in Heegaard Floer homology

Andrew Manion

Algebraic & Geometric Topology 24 (2024) 1157–1182
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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