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SUMMARY:Homology gradients of Bestvina--Brady Groups - Sam Fisher\, Univer
 sity of Oxford
DTSTART:20230224T160000Z
DTEND:20230224T170000Z
UID:TALK183893@talks.cam.ac.uk
CONTACT:Macarena Arenas
DESCRIPTION:Let P be a numerical invariant of a topological space\, let X 
 be a space\, and let (X_i) be a (residual) tower of covers of finite degre
 e d_i. The P-gradient associated to the pair X\, (X_i) is the limit of P(X
 _i) / d_i as i tends to infinity. The three most important questions to an
 swer when studying P-gradients are: Does the limit exist? Does it depend o
 n the choice of tower? Can we relate the limit to another known invariant?
  When P is the nth rational Betti number\, the answer to all these questio
 ns is provided by Lück's celebrated Approximation Theorem\, which states 
 that the limit always equals the nth L^2 Betti number.\nIn this talk\, we 
 will discuss several gradient invariants and the many open problems in thi
 s area. We will focus primarily on the mod-p homology gradients\, where ou
 r main result will be a computation of these invariants for Bestvina--Brad
 y groups\, and more generally kernels of maps from Raags to Z. If time per
 mits\, we will also mention a connection with algebraic fibring. This is j
 oint work with Sam Hughes and Ian Leary. \n
LOCATION:MR13
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