Singular TQFTs, foams and type D arc algebras

Abstract

We combinatorially describe the $2$-category of singular cobordisms, called (rank one) foams, which governs the functorial version of Khovanov homology. As an application we topologically realize the type $\mathrm{D}$ arc algebra using this singular cobordism construction.

arXiv comment52 pages, many colored figures, revised version, to appear in Doc. Math., comments welcome