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SUMMARY:Duality groups and Cohen-Macaulay spaces - Ric Wade (University of
  Oxford)
DTSTART:20221021T124500Z
DTEND:20221021T134500Z
UID:TALK182810@talks.cam.ac.uk
CONTACT:76015
DESCRIPTION:Via Poincaré duality\, fundamental groups of aspherical manif
 olds have (appropriately shifted) isomorphisms between their homology and 
 cohomology. In a 1973 Inventiones paper\, Bieri and Eckmann defined a broa
 der notion of a duality group\, where the isomorphism between homology and
  cohomology can be twisted by an object called a dualizing module. Example
 s of these groups in geometric group theory (after passing to a finite-ind
 ex subgroup) include $GL(n\,/mathbb{Z})$\, mapping class groups\, and auto
 morphism groups of free groups.\n\nEvery example of a duality group that w
 e know of has a classifying space satisfying a local condition called the 
 Cohen-Macaulay property. Such spaces also satisfy weaker (twisted) version
 s of Poincaré duality via their local homology sheaves (or local cohomolo
 gy cosheaves). However it is not clear on how to directly link the topolog
 ical and algebraic duality results. The goal of the talk is to explain mor
 e about the words used in the above paragraphs and say where we have got t
 o so far with this problem. Based on joint work with Thomas Wasserman.\n
LOCATION:MR13
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