Injectivity radius of manifolds with a Lie structure at infinity
Annales mathématiques Blaise Pascal, Volume 29 (2022) no. 2, pp. 235-246.

Using Lie groupoids, we prove that the injectivity radius of a manifold with a Lie structure at infinity is positive. This relies on the integrability of the corresponding Lie algebroid, a well-known result that we prove explicitly by regarding manifolds with corners as particular instances of orbifolds.

À l’aide des groupoïdes de Lie, on montre que le rayon d’injectivité d’une variété munie d’une structure de Lie à l’infini est strictement positif. La démonstration s’appuie sur l’intégrabilité de l’algébroïde de Lie correspondant, un résultat bien connu que l’on établit directement en regardant les variétés à coins comme des cas particuliers d’orbifolds.

Published online:
DOI: 10.5802/ambp.412
Classification: 53C22, 22A22
Keywords: Injectivity radius, Lie structure at infinity, Lie groupoid
Mot clés : Rayon d’injectivité, structure de Lie à l’infini, groupoïde de Lie
Quang-Tu Bui 1

1 Départment de Mathématiques Université du Québec à Montréal C.P. 8888, Succ. Centre-Ville Montréal (Québec) H3C 3P8 Canada
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Quang-Tu Bui. Injectivity radius of manifolds with a Lie structure at infinity. Annales mathématiques Blaise Pascal, Volume 29 (2022) no. 2, pp. 235-246. doi : 10.5802/ambp.412. https://ambp.centre-mersenne.org/articles/10.5802/ambp.412/

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