Rheinische Friedrich-Wilhelms-Universität Bonn

A quasihomomorphism is a map that satisfies the homomorphism relation up to bounded error. Fujiwara and Kapovich proved a rigidity result for quasihomomorphisms taking values in discrete groups, showing that all quasihomomorphisms can be built from homomorphisms and sections of bounded central extensions. We study quasihomomorphisms with values in real linear algebraic groups, and prove an analogous rigidity theorem.  Based on joint work with Sami Douba, Francesco Fournier Facio, and Simon Machado.

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.