Computing colored Khovanov homology

Fuente: arXiv
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Auteur principal: von Merkl, Karim Ritter
Format: Preprint
Publié: 2025
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author von Merkl, Karim Ritter
author_facet von Merkl, Karim Ritter
contents We compare eight versions of finite-dimensional categorifications of the colored Jones polynomial and show that they yield isomorphic results over a field of characteristic zero. As an application, we verify a physics-motivated conjectural formula for colored superpolynomials based on Poincaré polynomials of the Khovanov homology of cables. We also obtain a conjectural closed formula for the Poincaré series of the skein lasagna module of $\overline{\mathbb{CP}^2}$. Accompanying this note is an online database of colored superpolynomials.
format Preprint
id arxiv_https___arxiv_org_abs_2505_03916
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Computing colored Khovanov homology
von Merkl, Karim Ritter
Quantum Algebra
Geometric Topology
We compare eight versions of finite-dimensional categorifications of the colored Jones polynomial and show that they yield isomorphic results over a field of characteristic zero. As an application, we verify a physics-motivated conjectural formula for colored superpolynomials based on Poincaré polynomials of the Khovanov homology of cables. We also obtain a conjectural closed formula for the Poincaré series of the skein lasagna module of $\overline{\mathbb{CP}^2}$. Accompanying this note is an online database of colored superpolynomials.
title Computing colored Khovanov homology
topic Quantum Algebra
Geometric Topology
url https://arxiv.org/abs/2505.03916