Generic $\mathfrak{gl}_2$-foams, web and arc algebras
  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. 
Michael Ehrig, Catharina Stroppel and Daniel Tubbenhauer
math.GT math.RT