Stratifications and Actions of the Circle Group

Stratifications of topological spaces are often a useful tool to calculate different invariants of topological spaces. They also naturally arise in many cases. An instance of this is decomposing a CW complex by dimension of the cells. This gives rise to Cellular Homology, which is often much more computable than Singular Homology, but gives rise to isomorphic groups. In this talk, we will see some instances of stratifications and how they are useful.  Then we will use stratifications to try to better understand actions of the circle group on stable infinity categories.