Schedule
of talks:
Based on the book "Metric Spaces of non-positive curvature"
by M.Bridson and A.Hefliger.
Organizers in the Fall of 2001 are:
This term I hold "official" RAP office hours:
Tuesdays and Fridays 3-4pm, Illini Hall, Room 328
Appointments at other times are possible!! Call or
e-mail me to set an appointment.
Office phone number: (217)265-0633
E-mail: kapovich@math.uiuc.edu
WWW: http://www.math.uiuc.edu/~kapovich
Spring 2001 RAP "Sapaces of non-positive
curvature" page
News
We will have at least two outside speakers this semester
who will give talks on CAT(0) related topics in the Group Theory seminar
(Thursdays, 1pm):
Abstract:
Brian Bowditch has explained that Gromov's concept of
relative
hyperbolicity is actually a very direct generalization
of geometrically
finite Kleinian groups. A group G is relatively
hyperbolic if it admits
an action on a Gromov-hyperbolic space X which
is ``geometrically
finite'' in an appropriate sense.
Asli Yaman has recently shown that relatively hyperbolic
groups can be
completely characterized in terms of properties of their
action on the
boundary of X. If a group G admits
an action on a metrizable
compactum M satisfying certain properties, then
she shows that G is
relatively hyperbolic and that M is the boundary
of G.
We use this result to show that a certain class of CAT(0)
groups are
hyperbolic relative to their maximal abelian subgroups
of rank at least
two. The groups in question are those which act
properly and cocompactly
on CAT(0) spaces in which the flat Euclidean subspaces
are isolated.
Schedule
of talks:
Abstract: We will describe so called ``cubical
complexes" which are spaces obtained by gluing a collection of euclidean
cubes along isometries between their faces. An explicit combinatorial condition
will be given which ensures that such a complex is a CAT(0)-space.