Title: Bredon homology of partition posets, a theorem of Kuhn, and its $ku$ analogue
Speaker: Greg Arone
Speaker Info: University of Virginia
Abstract:
The symmetric powers of of the sphere spectrum $S$ form a sequence interpolating between $S$ and $HZ$. A theorem of Kuhn says that a homotopy spectral sequence associated with this filtration terminates at $E^2$. Around 2007, Kathryn Lesh and I constructed an analogous sequence of spectra interpolating between the connective K-theory spectrum $ku$ and $HZ$, and conjectured that an analogue of Kuhn’s theorem holds for this filtration. I will describe a new proof of Kuhn’s theorem, and a program for proving the $ku$ analogue. A key step in the proof is a calculation of the Bredon homology of the partition complex with coefficients in a general Mackey functor. This is joint work with Bill Dwyer and Kathryn Lesh.Date: Saturday, October 25, 2014