On donne une catégorification de l’évaluation symétrique des toiles 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 . 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.
We provide a finite-dimensional categorification of the symmetric evaluation of -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 . 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.
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Keywords: Link homology, quantum invariant, foams, Soergel bimodules
Mot clés : Homologie d’entrelacs, invariant quantiques, mousses, bimodules de Soergel
@article{JEP_2020__7__573_0, author = {Robert, Louis-Hadrien and Wagner, Emmanuel}, title = {Symmetric {Khovanov-Rozansky} link homologies}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {573--651}, publisher = {Ecole polytechnique}, volume = {7}, year = {2020}, doi = {10.5802/jep.124}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jep.124/} }
TY - JOUR AU - Robert, Louis-Hadrien AU - Wagner, Emmanuel TI - Symmetric Khovanov-Rozansky link homologies JO - Journal de l’École polytechnique — Mathématiques PY - 2020 SP - 573 EP - 651 VL - 7 PB - Ecole polytechnique UR - http://archive.numdam.org/articles/10.5802/jep.124/ DO - 10.5802/jep.124 LA - en ID - JEP_2020__7__573_0 ER -
%0 Journal Article %A Robert, Louis-Hadrien %A Wagner, Emmanuel %T Symmetric Khovanov-Rozansky link homologies %J Journal de l’École polytechnique — Mathématiques %D 2020 %P 573-651 %V 7 %I Ecole polytechnique %U http://archive.numdam.org/articles/10.5802/jep.124/ %R 10.5802/jep.124 %G en %F JEP_2020__7__573_0
Robert, Louis-Hadrien; Wagner, Emmanuel. Symmetric Khovanov-Rozansky link homologies. Journal de l’École polytechnique — Mathématiques, Tome 7 (2020), pp. 573-651. doi : 10.5802/jep.124. http://archive.numdam.org/articles/10.5802/jep.124/
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