Work

Surface Gluing with Signs and Gradings in Decategorified Heegaard Floer Theory

Year: 2023

Type: article

Abstract: A previous result about the decategorified bordered (sutured) Heegaard Floer invariants of surfaces glued together along intervals, generalizing the decategorified content of Rouquier and the author’s higher-tensor-product-based gluing theorem in cornered Heegaard Floer homology, was proved only over ${\mathbb{F}}_2$ and without gradings. In this paper we add signs and prove a graded version of the interval gluing theorem over ${\mathbb{Z}}$, enabling a more detailed comparison of these aspects of decategorified Heegaard Floer theory with modern work on non-semisimple 3d TQFTs in mathematics and physics.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnad238

Author: Andrew Manion

Institution: North Carolina State University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Higher Representation Theory and Heegaard Floer Homology