Categorifying Quiver Linking/Unlinking using CoHA Modules

Fuente: arXiv
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Main Author: van Garderen, Okke
Format: Preprint
Published: 2024
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author van Garderen, Okke
author_facet van Garderen, Okke
contents The knots-quivers correspondence is a relation between knot invariants and enumerative invariants of quivers, which in particular translates the knot operations of linking and unlinking to a certain mutation operation on quivers. In this paper we show that the moduli spaces of a quiver and its linking/unlinking are naturally related, giving a purely representation theoretic interpretation of these operations. We obtain a relation between the cohomologies of these spaces which is moreover compatible with a natural action of the Cohomological Hall Algebra. The result is a categorification of quiver linking/unlinking at the level of CoHA modules.
format Preprint
id arxiv_https___arxiv_org_abs_2409_05605
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Categorifying Quiver Linking/Unlinking using CoHA Modules
van Garderen, Okke
Algebraic Geometry
Representation Theory
16G20 (Primary), 14N35 (Secondary)
The knots-quivers correspondence is a relation between knot invariants and enumerative invariants of quivers, which in particular translates the knot operations of linking and unlinking to a certain mutation operation on quivers. In this paper we show that the moduli spaces of a quiver and its linking/unlinking are naturally related, giving a purely representation theoretic interpretation of these operations. We obtain a relation between the cohomologies of these spaces which is moreover compatible with a natural action of the Cohomological Hall Algebra. The result is a categorification of quiver linking/unlinking at the level of CoHA modules.
title Categorifying Quiver Linking/Unlinking using CoHA Modules
topic Algebraic Geometry
Representation Theory
16G20 (Primary), 14N35 (Secondary)
url https://arxiv.org/abs/2409.05605