A rational pullback decomposition for homeomorphism groups

Using the foundations for embedding calculus discussed in Manuel Krannich's lecture series, one can obtain a rational description of the classifying spaces of certain homeomorphism groups as a pullback. We will explain this, and give applications to Pontryagin–Weiss classes as well as a variant of the Burghelea–Lashof splitting theorem. This is joint work with Manuel Krannich.