Étale groupoids as germ grupoids and their applications to coarse geometry

Description:  Every étale topological groupoid G gives rise to an inverse semigroup equipped with a natural representation on the space of units of G. The germs of such representation can be given the structure of an étale groupoid which turns out to be isomorphic to G. We extend this construction to `wide' inverse semigroups over a topological space, which allows one to effectively construct étale groupoid extensions by extending or modifying the underlying inverse semigroup. We use this machinery to construct an étale groupoid which is an extension of a given groupoid in a way that its unit space is the Stone-Čech compactification of the unit space of the given groupoid, this extension generalizes the translation groupoid of Skandalis, Tu, and Yu used in their study of the Novikov conjecture by coarse geometric methods. Date:  2007-10-23 Start Time:   14:45 Speaker:  Dmitry Matsnev (IST) Institution:  IST Place:  Sala 5.5 Research Groups: -Algebra, Logic and Topology See more:   <Main>