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DTSTART:19700329T010000
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CATEGORIES:Junior Geometry Seminar
SUMMARY:Homology gradients of Bestvina--Brady Groups - Sam
Fisher\, University of Oxford
DTSTART;TZID=Europe/London:20230224T160000
DTEND;TZID=Europe/London:20230224T170000
UID:TALK183893AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/183893
DESCRIPTION:Let P be a numerical invariant of a topological sp
ace\, let X be a space\, and let (X_i) be a (resid
ual) tower of covers of finite degree d_i. The P-g
radient associated to the pair X\, (X_i) is the li
mit of P(X_i) / d_i as i tends to infinity. The th
ree most important questions to answer when studyi
ng P-gradients are: Does the limit exist? Does it
depend on the choice of tower? Can we relate the l
imit to another known invariant? When P is the nth
rational Betti number\, the answer to all these q
uestions is provided by Lück's celebrated Approxim
ation Theorem\, which states that the limit always
equals the nth L^2 Betti number.\nIn this talk\,
we will discuss several gradient invariants and th
e many open problems in this area. We will focus p
rimarily on the mod-p homology gradients\, where o
ur main result will be a computation of these inva
riants for Bestvina--Brady groups\, and more gener
ally kernels of maps from Raags to Z. If time perm
its\, we will also mention a connection with algeb
raic fibring. This is joint work with Sam Hughes a
nd Ian Leary. \n
LOCATION:MR13
CONTACT:Macarena Arenas
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