Symmetric Khovanov-Rozansky link homologies
Journal de l’École polytechnique — Mathématiques, Volume 7 (2020), pp. 573-651.

We provide a finite-dimensional categorification of the symmetric evaluation of 𝔰𝔩 N -webs using foam technology. As an output we obtain a symmetric link homology theory categorifying the link invariant associated to symmetric powers of the standard representation of 𝔰𝔩 N . The construction is made in an equivariant setting. We prove also that there is a spectral sequence from the Khovanov-Rozansky triply graded link homology to the symmetric one and provide along the way a foam interpretation of Soergel bimodules.

On donne une catégorification de l’évaluation symétrique des toiles 𝔰𝔩 N en utilisant les mousses. On en déduit des théories homologiques d’entrelacs qui catégorifient les invariants quantiques d’entrelacs associés aux puissances symétriques de la représentation standard de 𝔰𝔩 N . Ces théories sont obtenues dans un cadre équivariant. On montre qu’il existe des suites spectrales de l’homologie triplement graduée de Khovanov-Rozansky vers ces homologies symétriques. On donne aussi une interpretation des bimodules de Soergel en terme de mousses.

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DOI: 10.5802/jep.124
Classification: 57R56,  57M27,  17B10,  17B37
Keywords: Link homology, quantum invariant, foams, Soergel bimodules
Louis-Hadrien Robert 1; Emmanuel Wagner 2

1 Université de Genève 2–4 rue du lièvre, 1227 Genève, Switzerland Cogitamus Laboratory
2 Univ Paris Diderot, IMJ-PRG, UMR 7586 CNRS F-75013, Paris, France Université de Bourgogne Franche-Comté, IMB, UMR 5584 21000 Dijon, France Cogitamus Laboratory
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {Symmetric {Khovanov-Rozansky} link homologies},
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Louis-Hadrien Robert; Emmanuel Wagner. Symmetric Khovanov-Rozansky link homologies. Journal de l’École polytechnique — Mathématiques, Volume 7 (2020), pp. 573-651. doi : 10.5802/jep.124. https://jep.centre-mersenne.org/articles/10.5802/jep.124/

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