2009 Topology Seminar - 13

Given a reasonable filtration of spaces F_0, F_1,..., F_n, and a homology theory H, we define what it means to split the filtration with respect to H and then give a criterion for when this is possible. We strongly refine this criterion to decide when the filtration splits stably (and hence splits with respect to any homology theory). Many examples will be discussed (like Steenrod splitting, snaith splitting, configuration spaces, commuting tuples in lie groups, Miller splitting of unitary groups, etc). This work is by and with Stylian Zanos (Lille).