Bonn Topology Group - Abstracts

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Talk

December 11th 2018
Benjamin Böhme (RFWU Bonn): Idempotent splittings of G-equivariant commutative ring spectra.

Abstract

Let G be a finite group. Given a G-equivariant commutative ring spectrum, any idempotent element of its homotopy ring gives rise to a splitting of the spectrum into "idempotent summands". These summands behave in a surprising way: other than in commutative algebra or non-equivariant spectra, they need no inherit a commutative ring structure. I will discuss this phenomenon in detail for the equivariant sphere spectrum and for equivariant topological K-theory and present a simple group-theoretic characterization of the "best possible" ring structures on their idempotent summands. An important ingredient is the classification of idempotents in the (p-local) representation ring of G, which was not previously known and may be of independent interest.

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