Fundamental groupoids of -graphs.
Pask, David, Quigg, John, Raeburn, Iain (2004)
The New York Journal of Mathematics [electronic only]
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Pask, David, Quigg, John, Raeburn, Iain (2004)
The New York Journal of Mathematics [electronic only]
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Jean Pradines (2004)
Open Mathematics
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Starting with some motivating examples (classical atlases for a manifold, space of leaves of a foliation, group orbits), we propose to view a Lie groupoid as a generalized atlas for the “virtual structure” of its orbit space, the equivalence between atlases being here the smooth Morita equivalence. This “structure” keeps memory of the isotropy groups and of the smoothness as well. To take the smoothness into account, we claim that we can go very far by retaining just a few formal properties...
Baez, John C., Hoffnung, Alexander E., Walker, Christopher D. (2010)
Theory and Applications of Categories [electronic only]
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Anders Kock (2003)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Ladislav Nebeský (2006)
Czechoslovak Mathematical Journal
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In this paper, by a travel groupoid is meant an ordered pair such that is a nonempty set and is a binary operation on satisfying the following two conditions for all : Let be a travel groupoid. It is easy to show that if , then if and only if . We say that is on a (finite or infinite) graph if and Clearly, every travel groupoid is on exactly one graph. In this paper, some properties of travel groupoids on graphs are studied.
Ronald Brown, Osman Mucuk (1995)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Jung Rae Cho, Jeongmi Park, Yoshio Sano (2014)
Czechoslovak Mathematical Journal
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The notion of travel groupoids was introduced by L. Nebeský in 2006 in connection with a study on geodetic graphs. A travel groupoid is a pair of a set and a binary operation on satisfying two axioms. We can associate a graph with a travel groupoid. We say that a graph has a travel groupoid if the graph associated with the travel groupoid is equal to . Nebeský gave a characterization of finite graphs having a travel groupoid. In this paper, we study travel groupoids on infinite...