The diagrammatic Soergel category and sl(2) and sl(3) foams
Pedro Vaz
TL;DR
This paper constructs two functors from Elias and Khovanov's diagrammatic Soergel category to categories of sl(2) and sl(3) foams, bridging diagrammatic algebra and topological quantum field theories.
Contribution
It introduces two new functors connecting the diagrammatic Soergel category to sl(2) and sl(3) foam categories, expanding the categorical framework for link invariants.
Findings
Established functors from Soergel category to sl(2) and sl(3) foam categories.
Bridged algebraic and topological approaches in categorification.
Provided tools for further exploration of link homologies.
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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Geometric and Algebraic Topology