The diagrammatic Soergel category and sl(2) and sl(3) foams

2009/09/18 by Pedro Vaz, Vaz, Pedro
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.GT #math.QA

paper · pdf · doi:10.48550/arxiv.0909.3495

v4, minor changes, referee's comments implemented. v3, 20 pages, lots of figures, remark about the general case rewritten, one redundant relation removed from definition of SC1 and minor typos

arxiv created 2010/04/08 · arxiv updated 2010/04/09

Abstract

We define two functors from Elias and Khovanov's diagrammatic Soergel category, one targeting Clark-Morrison-Walker's category of disoriented sl(2) cobordisms and the other the category of (universal) sl(3) foams.

Related

• The diagrammatic Soergel category and sl(N)-foams, for N > 3
• sl(3)-Foams and the Khovanov-Lauda categorification of quantum sl(k)
• The \mathfraksl_n foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality
• A diagrammatic presentation of the category 3Cob
• Lectures on SL(3) foams and link homology