When free algebras are not free modules and the weird world of equivariant algebra

Abstract: In homological algebra, we take for granted that the free $\mathbb{Z}$-algebra $\mathbb{Z}$[x] is also free as a $\mathbb{Z}$-module. This fact is crucial for certain computations in homotopy theory. We want to make some of these same computations in equivariant homotopy theory, where $\mathbb{Z}$-algebras are replaced by incomplete Tambara functors and $\mathbb{Z}$-modules are replaced by Mackey functors. However, a free incomplete Tambara functor is almost never (i.e. with probability zero) free as a Mackey functor! In this talk, I will explain this oddity of equivariant homotopy theory and one way to resolve it. This is joint work with Mike Hill and J.D. Quigley.

algebraic topologycategory theoryK-theory and homology

Audience: researchers in the topic

Rochester topology seminar