Wed, 22 Jun 2011
16:00 -
17:00
SR1
Parallelogram Law for Isometries of CAT(0)-spaces
Moritz Rodenhausen
(Rheinische Friedrich-Wilhelms-Universität Bonn)
Abstract
In euclidean space there is a well-known parallelogram law relating the
length of vectors a, b, a+b and a-b. In the talk I give a similar formula
for translation lengths of isometries of CAT(0)-spaces. Given an action of
the automorphism group of a free product on a CAT(0)-space, I show that
certain elements can only act by zero translation length. In comparison to
other well-known actions this leads to restrictions about homomorphisms of
these groups to other groups, e.g. mapping class groups.