Loday Constructions of Tambara functors

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• Birgit Richter (Universität Hamburg)
• Monday 12 June 2023, 14:30-15:30
• Seminar Room 1, Newton Institute.

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This paper is  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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