Pure PGR Seminar - Bounded Cohomology, Vlad Vankov (Southampton) Seminar

Event details

The circle is a topological space of great importance and interest both in algebraic topology and geometric group theory. We shall explore the question: which groups can act on the circle? Every group can be made to act on the circle by making every group element act as the identity map, therefore we will restrict our attention to non-trivial actions, which suddenly makes this question worth asking. The group SL(2,Z) can act non-trivially on the circle, whereas for n > 2, SL(n,Z) cannot. We shall see that this is a consequence of the latter groups being lattices in "higher rank Lie groups".