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Graded Tambara functors

Banff International Research Station for Mathematical Innovation and Discovery

Let \(E\) be a \(G\)-spectrum for a finite group \(G\). It's reasonably well understood that the 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, which is more structure than just a Mackey functor with commutative multiplication. I will discuss work with 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.

Mathematics; Algebraic topology; Category theory; homological algebra

video/mp4

Author affiliation: Vanderbilt University

2016-11-22

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59764

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/