Does anyone know a source that discusses dualizing complexes and six-functor stuff in the context of parametrized spectra? My understanding is that for a map f:X->Y with finite fibers there exists a certain fiberwise finite spectrum \omega_f with nice properties wrt pushforward and that if f has poincare complexes as fibers then \omega_f identifies with the fiberwise spivak bundle.
The paper "Duality for Smooth Families in Equivariant Stable Homotopy Theory" by Po Hu goes a long way in this direction but it's not quite what I want.
Hi, does anyone have an idea how to produce the spin orientation of ko from the spin^c orientation of ku using homotopy theoretical methods (i.e. without knowledge of Clifford modules and stuff)?
@DominikAbsmeier is it possible to produce the spin^c orientation of ku without using Clifford modules? (that doesn't obstruct your question, of course; I'm just curious)
@ArunDebray yes, I have a method to actually produce it as an E_infty orientation through homotopy theoretical means and Michael Joachim has an argument based on operator algebra stuff if I recall that correctly
