3-dimensional defect TQFTs and their tricategories

2016, March 3
Nils Carqueville, Catherine Meusburger, Gregor Schaumann
arxiv preprint arxiv:1603.01171
We initiate a systematic study of 3-dimensional `defect’ topologi-
cal quantum field theories, that we introduce as symmetric monoidal
functors on stratified and decorated bordisms. For every such functor
we construct a tricategory with duals, which is the natural categori-
cation of a pivotal bicategory. This captures the algebraic essence
of defect TQFTs, and it gives precise meaning to the fusion of line
and surface defects as well as their duality operations. As examples,
we discuss how Reshetikhin-Turaev and Turaev-Viro theories embed
into our framework, and how they can be extended to defect TQFTs.