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Loday Constructions of Tambara functors

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HHHW06 - HHH follow on: Homotopy: fruit of the fertile furrow

This paper is  hopefully a first step towards generalizing the Loday construction forcommutative rings  and ring spectra to the equivariant context. 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-symmetricmonoidal 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 tensoringa 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 ofits properties and describe it in examples.  

This talk is part of the Isaac Newton Institute Seminar Series series.

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