Abstract

In 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 $\Delta$-twisted simplicial sets.