Groupoids and Noncommutative Geometry Seminar 

15/11/2007, 13:30 — 14:30 — Room P3.10, Mathematics Building
Dmitry Matsnev, CAMGSD

Étale groupoids as germ groupoids and applications (part III)

Every etale 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 etale 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 etale groupoid extensions by extending or modifying the underlying inverse semigroup. We use this machinery in order to provide a simpler construction of Paterson's universal groupoid of an inverse semigroup, and also of the \'etale groupoid that arises by applying Stone--Cech compactification to the unit space of the pair groupoid on a set, which is the translation groupoid of Skandalis, Tu, and Yu used in their study of the Novikov conjecture by coarse geometric methods.