Abstract:
We describe a bordered version of totally twisted Khovanov homology. We first twist Roberts's type D structure by adding a vertical type D structure which generalizes the vertical map in twisted tangle homology. One of the distinct advantages of our type D structure is that it is homotopy equivalent to a type D structure supported on spanning tree generators. We also describe how to twist Roberts's type A structure for a left tangle in such a way that pairing our type A and type D structures will result in the totally twisted Khovanov homology. Analogous to the type D structure, there is a spanning-tree-like model for the type A structure.
