Stability and invariants of Hilsum-Skandalis maps
By J. Mrčun. 2005
58 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Mathematical Physics, Pathology and Forensic Medicine
View Paper: https://www.semanticscholar.org/paper/ad139e0af83536dd4824f42369fbed9f91856487
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In Algebra and Number Theory
In Mathematical Physics
In Pathology and Forensic Medicine
Citations in the corpus
- Lie groupoids and their orbispaces (2012, unknown): “Some references for this material are [21] and [22].”
- n-Groupoids and Stacky Groupoids (2008, background): “Let T ′ be a sub-simplicial set obtained by deleting one l -simplex from T (without its boundary, and T ′ → T includes the case of → ∆[0]).”