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SUMMARY:Growth gap\, amenability and coverings
DTSTART;VALUE=DATE-TIME:20181210T153000Z
DTEND;VALUE=DATE-TIME:20181210T164500Z
DTSTAMP;VALUE=DATE-TIME:20210414T004557Z
UID:indico-event-4167@indico.math.cnrs.fr
DESCRIPTION:\n Let Γ be a group acting by isometries on a proper metric s
pace (X\,d). The critical exponent δΓ(X) is a number which measures the
complexity of this action. The critical exponent of a subgroup Γ'<Γ is h
ence smaller than the critical exponent of Γ. When does equality occur? I
t was shown in the 1980s by Brooks that if X is the real hyperbolic space\
, Γ' is a normal subgroup of Γ and Γ is convex-cocompact\, then equalit
y occurs if and only if Γ/Γ' is amenable. At the same time\, Cohen and G
rigorchuk proved an analogous result when Γ is a free group acting on its
Cayley graph.\n When the action of Γ on X is not cocompact\, showing tha
t the equality of critical exponents is equivalent to the amenability of
Γ/Γ' requires an additional assumption: a "growth gap at infinity". I wi
ll explain how\, under this (optimal) assumption\, we can generalize the r
esult of Brooks to all groups Γ with a proper action on a Gromov hyperbol
ic space.\n Joint work with R. Coulon\, R. Dougall and B. Schapira.\n\n\nh
ttps://indico.math.cnrs.fr/event/4167/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/4167/
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