Khovanov homology for virtual tangles and applications

Abstract

We extend the cobordism based categorification of the virtual Jones polynomial to virtual tangles. This extension is combinatorial and has semi-local properties. We use the semi-local property to prove an applications, i.e. we give a discussion of Lee's degeneration of virtual homology.

37 pages, lots of figures, followup of the paper arXiv:1111.0609

References in corpus (9)

• Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m)
• The sl_3 web algebra
• The Karoubi envelope and Lee's degeneration of Khovanov homology
• The ${\mathfrak{sl}}_n$ foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality
• Diagrams for perverse sheaves on isotropic Grassmannians and the supergroup SOSP(m|2n)
• ${\mathfrak{gl}}_n$-webs, categorification and Khovanov-Rozansky homologies
• The sl(N)-web algebras and dual canonical bases
• A large family of indecomposable projective modules for the Khovanov-Kuperberg algebra of $s{l}_3$-webs
• The Khovanov Complex for Virtual Links

Cited by in corpus (7)

• Computations of the slice genus of virtual knots
• Unoriented Virtual Khovanov Homology
• Steenrod square for virtual links toward Khovanov-Lipshitz-Sarkar stable homotopy type for virtual links
• Khovanov-Lipshitz-Sarkar homotopy type for links in thickened surfaces
• Ascent concordance
• Khovanov-Lipshitz-Sarkar homotopy type for links in thickened higher genus surfaces
• On the virtual Rasmussen invariant