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SUMMARY:Partial categories and directed path spaces -- a proposed construc
 tion of orbit categories for p-local finite groups
DTSTART:20190305T101500
DTEND:20190305T111500
DTSTAMP:20260406T194543Z
UID:4d7a2e799b448f3945775fd8efd820d6353a955fa63b9976670ea487
CATEGORIES:Conferences - Seminars
DESCRIPTION:Sune Precht Reeh\nGiven a finite group G the orbit category of
  G consists of all transitive G-sets and equivariant maps between them. As
 ide from algebra the orbit category has also proved very useful in topolog
 y for describing G-equivariant homotopy theory.\nFor a saturated fusion sy
 stem/p-local finite group F with Sylow subgroup S the existing constructio
 ns of an orbit category for F only makes sense for subgroups of S that are
  "sufficiently large". In this talk I will propose a construction of an or
 bit category for F that works for all subgroups of S\, but the result will
  be a "partial" category (to be defined during the talk) where composition
  of morphisms is only partially defined. The construction builds upon the 
 theorem of Andy Chermak that a saturated fusion system is always realized 
 by a (suitably unique) partial group.\nEvery partial category gives rise t
 o a actual category enriched in simplicial sets via a very explicit proced
 ure using a sort of directed path spaces. We shall see that the proposed o
 rbit category restricts to a classical category when considering "sufficie
 ntly large" subgroups of S and that we recover the old definition of an or
 bit category for F.\nThis joint project with Rémi Molinier is very much a
  work in progress\, and as such the talk will contain many more conjecture
 s than theorems.
LOCATION:MA A1 12 https://plan.epfl.ch/?room=MAA112
STATUS:CONFIRMED
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