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SUMMARY:On the global dimension of categories of Mackey functors - David B
 arnes (Queen's University Belfast)
DTSTART:20250514T091500Z
DTEND:20250514T101500Z
UID:TALK230536@talks.cam.ac.uk
DESCRIPTION:The homotopy groups of a G-spectrum form a (graded) G-Mackey f
 unctor\, so calculations of Mackey functors and (derived) maps between the
 m occur throughout stable equivariant homotopy theory. A natural question 
 is to ask: how complicated is the homological algebra of this category? A 
 good measure of this complexity is the global dimension (also called the p
 rojective dimension or homological dimension). For finite groups the globa
 l dimension of G-Mackey functors is infinite. If we work rationally\, howe
 ver\, the global dimension is zero and hence the category is semi-simple. 
 Thus for finite groups\, we only see the two extremes.&nbsp\;\nIn this tal
 k we work rationally and generalise in two directions. Firstly\, we genera
 lise the group to the compact Lie and profinite case. Secondly\, we return
  to the case of finite groups but now work with the incomplete Mackey func
 tors from Kedziorek&rsquo\;s talk. We show that arbitrary global dimension
  occurs in all of these cases and give topological methods for calculating
  the global dimension.
LOCATION:Seminar Room 1\, Newton Institute
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