2004/01/15 by Carlo A. Rossi, C. A. Rossi, Rossi, C. A. · 1 citation
Mathematics · Medicine · Physics and Astronomy · #58H05 #81Q70 #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Ophthalmology and Eye Disorders #math-ph #math.DG #math.MP #msc:58H05 #msc:81Q70
paper · pdf · doi:10.48550/arxiv.math/0401182
Some modifications of the introduction; retrieved a small subsection; added a new section concerning Hilsum-Skandalis morphisms and Hilsum-Skandalis generalized gauge transformations; added some citations
openalex publication_date 2004/01/15 · arxiv created 2004/02/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the computations done in \citeC1, where I introduced and discussed what I called the groupoid of generalized gauge transformations, viewed as a groupoid over the objects of the category BunG,M of principal G-bundles over a given manifold M, I develop in this paper the same ideas for the more general case of \em principal \calG-bundles or principal bundles with structure groupoid \calG, where now \calG is a Lie groupoid in the sense of \citeMoer2. Most of the concepts introduced in \citeC1 can be translated almost verbatim in the framework of principal bundles with structure groupoid \calG; in particular, the key r�le for the construction of generalized gauge transformations is again played by (the equivalent in the framework of principal bundles with groupoid structure of) the division map fP. Of great importance are also the generalized conjugation in a groupoid and the concept of (twisted) equivariant maps between groupoid-spaces.