Lie groupoids of mappings taking values in a Lie groupoid

Habib Amiri; Helge Glöckner; Alexander Schmeding

Displaying similar documents to “Lie groupoids of mappings taking values in a Lie groupoid”

The monodromy groupoid of a Lie groupoid

Ronald Brown, Osman Mucuk (1995)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Travel groupoids

Ladislav Nebeský (2006)

Czechoslovak Mathematical Journal

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In this paper, by a travel groupoid is meant an ordered pair $(V, *)$ such that $V$ is a nonempty set and $*$ is a binary operation on $V$ satisfying the following two conditions for all $u, v \in V$ : $(u * v) * u = u; if (u * v) * v = u, then u = v .$ Let $(V, *)$ be a travel groupoid. It is easy to show that if $x, y \in V$ , then $x * y = y$ if and only if $y * x = x$ . We say that $(V, *)$ is on a (finite or infinite) graph $G$ if $V (G) = V$ and $E (G) = {{u, v} u, v \in V and u \neq u * v = v} .$ Clearly, every travel groupoid is on exactly one graph. In this paper, some properties of travel groupoids on graphs are studied.

A note on Lie algebroids which arise from groupoid actions

Kirill Mackenzie (1987)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Integrability obstructions for extensions of Lie algebroids

Kirill Mackenzie (1987)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Orbit projections of proper Lie groupoids as fibrations

Armin Rainer (2009)

Czechoslovak Mathematical Journal

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Let $𝒢 ⇉ M$ be a source locally trivial proper Lie groupoid such that each orbit is of finite type. The orbit projection $M \to M / 𝒢$ is a fibration if and only if $𝒢 ⇉ M$ is regular.

Exponential mapping for Lie groupoids

Jan Kubarski (1982)

Colloquium Mathematicae

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