Generic ${\mathfrak{gl}}_2$-foams, web and arc algebras

Abstract

We define parameter dependent ${\mathfrak{gl}}_2$-foams and their associated web and arc algebras, and verify that they specialize to several known ${\mathfrak{sl}}_2$ or ${\mathfrak{gl}}_2$ constructions related to higher link and tangle invariants. Moreover, we show that all these specializations are equivalent, and we deduce several applications, e.g. we discuss the consequences for the associated link and tangle invariants, and their functoriality.

Section on functoriality added and other significant changes, 42 pages, many colored figures, comments welcome

References in corpus (5)

• 2-Kac-Moody algebras
• Super $q$-Howe duality and web categories
• Deformations of colored sl(N) link homologies via foams
• TQFT with corners and tilting functors in the Kac-Moody case
• The universal sl(2) cohomology via webs and foams

Cited by in corpus (4)

• The Blanchet-Khovanov algebras
• Integral presentations of quantum lattice Heisenberg algebras
• Decorated one-dimensional cobordisms and tensor envelopes of noncommutative recognizable power series
• Two-block Springer fibers of types C and D: a diagrammatic approach to Springer theory