Robin Stoll: A rational model for the fiberwise THH-transfer

Abstract.

I will report on work in progress joint with Florian Naef and Nils Prigge in which we produce, for a map \(f\) of spaces over a space \(B\) such that \(f\) has compact fibers, a rational model for the fiberwise transfer of fiberwise THH, considered as a map of parametrized spectra over \(B\). It is constructed in terms of a \(C_\infty\)-model for the map \(f\). I will also indicate which consequences this might have for graph complex classes in the rational cohomology of classifying spaces of certain manifolds.