Khovanov homology as a 4-category; Khovanov skein modules for
4-manifolds
Kevin Walker
The Khovanov homology groups of a link in S^3 can be viewed as the
4-morphisms of a 4-category. This 4-category possesses strong duality
properties—similar to a 2-category being pivotal. These duality
properties allow one to construct skein modules for 4-manifolds based
on Khovanov homology. These skein modules are in some sense a
categorification of the Witten-Resetikhin-Turaev TQFT based on SU(2).
Along the way, we also obtain a simple formula for the Khovanov
homology of a connect sum of links. (This is joint work with Scott
Morrison.)