Let
be
an irreducible Artin–Tits group of spherical type. We show that the periodic elements
of
and the elements preserving some parabolic subgroup
of act elliptically on the
additional length graph ,
a hyperbolic, infinite diameter graph associated
to constructed by Calvez
and Wiest to show that
is acylindrically hyperbolic. We use these results to find an element
such that
for every proper standard
parabolic subgroup
of . The
length of
is uniformly bounded with respect to the Garside generators, independently
of .
This allows us to show that, in contrast with the Artin generators case, the sequence
of
exponential growth rates of braid groups, with respect to the Garside generating set,
goes to infinity.
PDF Access Denied
We have not been able to recognize your IP address
18.221.85.33
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.