Bonn Topology Group - Abstracts

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Talk

December 12, 2023
Nikolai Konovalov (MPIM Bonn): Algebraic Goodwillie spectral sequence

Abstract

The spectral Lie operad is the Koszul dual operad to the cocommutative cooperad in the category of spectra. A spectral Lie algebra is an algebra over the spectral Lie operad. M. Behrens and J. Kjaer constructed so-called Dyer-Lashof-Lie power operations acting on the mod-p homology groups of a spectral Lie algebra. However, they computed relations between these operations only for p=2. In my talk, I will explain how to compute the desired relations for any prime by using functor calculus in the category of simplicial restricted Lie algebras. The latter category might be thought of as an algebraic approximation of the category of spaces, and so, algebraic calculations may also be helpful in understanding of the topological Goodwillie spectral sequence.