Constructing oriented TQFTs from twisted pivotal tensor categories

The cobordism hypothesis classifies n-dimensional oriented TQFTs in terms of SO(n) homotopy fixed point data. An SO(2) homotopy fixed point structure on a finite tensor category gives rise to a twisted pivotal structure (a more general notion than a pivotal structure). In this talk, I will illustrate how the usual skein theory (also called string nets) of a pivotal tensor category can be generalized to the twisted pivotal setting, yielding new 2d oriented TQFTs. This is joint work with Ben Haioun and Filippos Sytilidis.