Birgit Richter (Hamburg): Loday Constructions of Tambara functors

This talk was part of the conference "Homotopy theory, K-theory, and trace methods" held in July 2023 at Radboud University, Nijmegen, The Netherlands in honor of Bjørn Ian Dundas' 60th birthday.

Abstract: Brun showed that pi_0 of every genuine commutative G ring spectrum is a G-Tambara functor. We define a Loday construction for G-Tambara functors for any finite group G. This definition builds on the Hill-Hopkins notion of a G-symmetric monoidal category and the work of Mazur, Hill-Mazur and Hoyer who prove that for any finite group and any G-Tambara functor R there is a compatible definition of tensoring a finite G-set X with R. We extend this to a tensor product of a G-Tambara functor with a finite simplicial G-set, defining the Loday construction this way. We investigate some of its properties and describe it in examples.