2005/06/23 by Janez Mrcun, J. Mrčun, Mrcun, Janez · 1 citation
Mathematics · Medicine · #22A22 #57R30 #57S25 #58H05 #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #math.DG #msc:22A22 #msc:57R30 #msc:57S25 #msc:58H05
paper · pdf · doi:10.48550/arxiv.math/0506484
Ph.D. thesis, Utrecht University, 1996
arxiv created 2005/06/23 · openalex publication_date 2005/06/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider principal bundles as generalized morphisms between topological groupoids. In the category of these generalized morphisms two topological groupoids are isomorphic if and only if they are Morita equivalent. We show that the fibers of a generalized morphism from H to G induce a singular foliation of the topological groupoid H, and we prove a Reeb-Thurston stability theorem for such foliations. Next, we use generalized morphisms to study some Morita invariants of topological groupoids, in particular the homotopy groups of a topological groupoid and the Connes convolution algebra of an etale groupoid.