PhD Defense: Benjamin Böhme

Title: Equivariant multiplications and idempotent splittings of G-spectra

Abstract:

My PhD research concerns multiplicative phenomena in equivariant stable homotopy theory. Equivariantly with respect to a finite group G, there are many different notions of a commutative ring spectrum. The idempotent summands of the genuine equivariant versions of the sphere spectrum and the topological K-theory spectra provide natural examples of such objects. I give a complete characterization of the best possible equivariant commutative ring structures on these summands. As an important step in my approach, I establish a classification of the idempotent elements in the (p-local) representation ring of G, which may be of independent interest.

Supervisor: Prof. Jesper Grodal, MATH, University of Copenhagen

Assessment Committee

Prof. (Chairman), Lars Hesselholt, University of Copenhagen

Prof. John Greenlees, University of Warwick

Ass. Prof, Andrew Blumberg, University of Austin, Texas