**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.

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