Gl2 Foam Functoriality and Skein Positivity

Hoel Queffelec

Gl2 Foam Functoriality and Skein Positivity

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arxiv 2209.08794 v1 pith:OUNK3JLK submitted 2022-09-19 math.QA math.GTmath.RT

Hoel Queffelec This is my paper · ORCID

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keywords functorialitypositivityproveresultskeinalgebrasargumentcategorical

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We prove full functoriality of Khovanov homology for tangled framed gl2 webs. We use this functoriality result to prove a strong positivity result for (orientable) surface skein algebras. The argument goes categorical and consists in proving that so-called linear complexes are stable under superposition.

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Monoidal categorification of genus zero skein algebras
math.RT 2025-05 conditional novelty 6.0 of 10

The relative Kauffman bracket skein algebra of a genus zero surface with boundary is isomorphic to a quantized K-theoretic Coulomb branch, yielding a convolution-product categorification.

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