  Many quantum invariants of knots and 3-manifolds (e.g. Jones polynomials) are
special cases of the Witten-Reshetikhin-Turaev 3D TQFT. The latter is in turn a
part of a larger theory - the Crane-Yetter 4D TQFT. In this work, we compute
the Crane-Yetter theory for all (smooth and oriented) surfaces with at least
one puncture. The results in general are constructed and called the categorical
center of higher genera.
