A type D structure in Khovanov homology
arXiv:1304.0463
Abstract
We describe the first part of a gluing theory for the bigraded Khovanov homology with integer coefficients. This part associates a type D structure to a tangle properly embedded in a half-space and proves that the homotopy class of the type D structure is an invariant of the isotopy class of the tangle. The construction is modeled off bordered Heegaard-Floer homology, but uses only combinatorial/diagrammatic methods
60 pgs, many figures; after first version appeared on the arXiv the author was contacted by Cotton Seed about his independent discovery of similar constructions - the second version includes a statement noting his work. The thirds version adds another type of relation to the algebra, necessary for the construction to succeed and makes additional, but minor improvements to exposition