The division map of principal bundles with groupoid structure and generalized gauge transformations

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dc.creatorRossi, C. A.
dc.date2004-01-15
dc.date2004-02-08
dc.date.accessioned2026-07-07T05:04:35Z
dc.date.available2026-07-07T05:04:35Z
dc.descriptionMotivated by the computations done in \cite{C1}, where I introduced and discussed what I called the groupoid of generalized gauge transformations, viewed as a groupoid over the objects of the category $\mathsf{Bun}_{G,M}$ 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 \cite{Moer2}. Most of the concepts introduced in \cite{C1} 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 $f_P$. Of great importance are also the generalized conjugation in a groupoid and the concept of (twisted) equivariant maps between groupoid-spaces.
dc.descriptionSome 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
dc.identifierhttps://arxiv.org/abs/math/0401182
dc.identifierhttp://arxiv.org/abs/math/0401182
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69861
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subject58H05; 81Q70
dc.titleThe division map of principal bundles with groupoid structure and generalized gauge transformations
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