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SUMMARY:Splittings in rational equivariant homotopy theory - Magdalena Ked
 ziorek (Radboud Universiteit Nijmegen)
DTSTART:20250512T104500Z
DTEND:20250512T114500Z
UID:TALK230515@talks.cam.ac.uk
DESCRIPTION:When G is a finite group\, rational genuine G-spectra split as
  a product of simpler categories: rational spectra with Weyl group actions
 . Algebraically\, this is the statement that rational Mackey functors are 
 semi-simple and the category of rational G-Mackey functors splits as a pro
 duct of module categories with Weyl group actions.&nbsp\;\nClassically\, t
 he homotopy theory of G-spectra depended on a choice of a universe - this 
 was modelled\, for example\, by the orthogonal G-spectra of Mandell and Ma
 y. In modern language\, Blumberg and Hill generalised the construction of 
 the homotopy theory of G-spectra and show that one can choose an additive 
 structure of it to be modelled by a homotopy type of an N_\\infty operad O
  (or equivalently a transfer system associated to O). Thus homotopy groups
  of a G-spectrum with additive structure given by O have those additive tr
 ansfers that are parametrised by O. We call such a structure a&nbsp\;G-Mac
 key functor for O.\nThe purpose of this talk is to describe splittings of 
 rational G-Mackey functors for incomplete transfer systems and discuss how
  this extends to the topological setting. This is joint work with Anna Mar
 ie Bohmann\, Dave Barnes and Mike Hill.
LOCATION:Seminar Room 1\, Newton Institute
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