95 research outputs found
Contracting Boundaries of CAT(0) Spaces
As demonstrated by Croke and Kleiner, the visual boundary of a CAT(0) group
is not well-defined since quasi-isometric CAT(0) spaces can have
non-homeomorphic boundaries. We introduce a new type of boundary for a CAT(0)
space, called the contracting boundary, made up rays satisfying one of five
hyperbolic-like properties. We prove that these properties are all equivalent
and that the contracting boundary is a quasi-isometry invariant. We use this
invariant to distinguish the quasi-isometry classes of certain right-angled
Coxeter groups.Comment: 27 pages, 8 figure
Convexity of parabolic subgroups in Artin groups
We prove that any standard parabolic subgroup of any Artin group is convex
with respect to the standard generating set
Automorphism groups of some affine and finite type Artin groups
We observe that, for each positive integer n > 2, each of the Artin groups of
finite type A_n, B_n=C_n, and affine type \tilde A_{n-1} and \tilde C_{n-1} is
a central extension of a finite index subgroup of the mapping class group of
the (n+2)-punctured sphere. (The centre is trivial in the affine case and
infinite cyclic in the finite type cases). Using results of Ivanov and Korkmaz
on abstract commensurators of surface mapping class groups we are able to
determine the automorphism groups of each member of these four infinite
families of Artin groups
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