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Graded Tambara functors

Presented by: 
Anna Marie Bohmann Vanderbilt University
Date: 
Thursday 16th August 2018 - 11:30 to 12:30
Venue: 
INI Seminar Room 1
Abstract: 
Let E be a G-spectrum for a finite group G. It's long been known that homotopy groups of E have the structure of "Mackey functors." If E is G commutative ring spectrum, then work of Strickland and of Brun shows that the zeroth homotopy groups of E form a "Tambara functor." This is more structure than just a Mackey functor with commutative multiplication and there is much recent work investigating nuances of this structure. I will discuss work with Vigleik Angeltveit that extends this result to include the higher homotopy groups of E. Specifically, if E has a commutative multiplication that enjoys lots of structure with respect to the G action, the homotopy groups of E form a graded Tambara functor. In particular, genuine commutative G ring spectra enjoy this property.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons