Algebra/Topology seminar

Benjamin Boehme, Multiplicativity of the idempotent splittings of the Burnside ring and the G-sphere spectrum 

Abstract: I provide a complete characterization of the equivariant commutative ring structures of all the idempotent summands of the G-equivariant
sphere spectrum, including their Hill-Hopkins-Ravenel norms, where G is any
finite group. My results describe explicitly how these structures depend on
the subgroup lattice and conjugation in G. Algebraically, my analysis
characterizes the multiplicative transfers on the localization of the Burnside
ring of G at any idempotent element, which is of independent interest to group
theorists. As an application, I obtain an explicit description of the
incomplete sets of norm functors which are present in the idempotent splitting
of the equivariant stable homotopy category.