Topology Seminar
Speaker: Aparajita Karmakar, IIT Bombay
Host: Rekha Santhanam
Title: Self-duality in the Burnside category - from spans to spectra
Time, day and date: 11:30:00 AM – 12:30:00 PM, Thursday, June 18
Venue: Room 215
Abstract: The Burnside category is a central object in equivariant homotopy and cohomology theories which encodes the structures of Mackey functors. Classically it is defined using spans of finite G-sets, a description that depends on the finiteness of G. Self-duality of the Burnside category is nearly transparent in its simplicity, but it is an algebraic artifact of a much deeper topological phenomenon. Each orbit has an equivariant suspension spectrum, and there is an equivalent definition of the Burnside category with morphisms given by stable equivariant morphisms. This definition is more general in the sense that it does not depend on the finiteness of the group. The stable orbit spectra satisfy an equivariant self-duality that induces the self duality of the Burnside category itself.