Logic Seminar
Todor Tsankov
University of Paris 7
Automatic continuity of homomorphisms and classifying separable group topologies
Abstract: It is an interesting phenomenon that for many Polish groups, the algebraic structure "remembers" the topology.
This can be given many meanings; perhaps the strongest is the following automatic continuity property: every
homomorphism into a separable group is continuous. This property can be thought of as a strengthening of the
well-studied in model theory small index property: a Polish group has the small index property iff every homomorphism
into $S_\infty$ is continuous. The automatic continuity property was introduced by Kechris and Rosendal, who also
developed a technique for verifying it. More recently, their technique was generalized to the continuous setting by Ben
Yaacov, Berenstein and Melleray and that allowed a new kind of "two-step" proofs of automatic continuity, most notably
for the unitary group and the automorphism group of a standard probability space, examples which were inaccessible
by previous methods.
Tuesday October 25, 2011 at 4:00 PM in SEO 427