Principal bundles with groupoid structure: local vs. global theory and nonabelian ucech cohomology

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dc.creatorRossi, C. A.
dc.date2004-04-25
dc.date.accessioned2026-07-07T05:07:42Z
dc.date.available2026-07-07T05:07:42Z
dc.descriptionThe aim of this paper is to review and discuss in detail local aspects of principal bundles with groupoid structure. Many results, in particular from the second and third section, are already known to some extents, but, due to the lack of a ``unified'' point of view on the subject, I decided nonetheless to (re)define all the main concepts and write all proofs; however, some results are reformulated in a more elegant way, using the division map and the generalized conjugation of a Lie groupoid. In the same framework, I discuss later generalized groupoids and Morita equivalences from a local point of view; in particular, I found a (so far as I know) new characterization of generalized morphisms coming from nonabelian ech cohomology, which allows one to view generalized morphisms as a generalization of classical descent data. I found also a factorization formula for the division map, which is the crucial point in the local formulation of Morita equivalences.
dc.description97 pages; mostly a review, but up to Section 4 there are some (as far as I know) new results, which I personally did not find anywhere else, or I found in a different shape
dc.identifierhttps://arxiv.org/abs/math/0404449
dc.identifierhttp://arxiv.org/abs/math/0404449
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70962
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subject53C10; 58H05
dc.titlePrincipal bundles with groupoid structure: local vs. global theory and nonabelian ucech cohomology
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