The role of p_1-structures in 3-dimensional Chern-Simons theories

Our recent paper~\cite{FST} with Claudia Scheimbauer uses the cobordism hypothesis to construct fully local Chern-Simons theories. Here we expose some physics motivations: Yang-Mills plus Chern-Simons in the bosonic case and the free Majorana-Weyl spinor field in the fermionic case. We also give expositions of tangential structures and invertible field theories, in particular the ‘gravitational Chern-Simons theory’ used by Witten to obtain topological field theories from the physical theories.