AbstractIn this talk, I will firstly review some kinds of homology such as weighted homology, $\delta$-homology, $\delta$-twisted homology. Then we define a $\Delta$-twisted homology on simplicial set, which can unify above homologies. Moreover, inspired by the classical twisted Cartesian product introduced by Barratte, Gugenheim, Moore, we also explore the fiber bundle structure on $\Delta$-tw...
AbstractI will describe a uniform construction to gauge a discrete invertible symmetry S in possibly non-topological (D+1)-dimensional quantum systems with higher-categorical and possibly non-invertible symmetries. The symmetry in the theory obtained after gauging contains a sub-category of universal topological defects, which we term as Theta defects. These defects are universal in the sense t...