[Le rayon d’injectivité des variétés munies d’une structure de Lie à l’infini]
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.
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.
Keywords: Injectivity radius, Lie structure at infinity, Lie groupoid
Mot clés : Rayon d’injectivité, structure de Lie à l’infini, groupoïde de Lie
@article{AMBP_2022__29_2_235_0,
author = {Bui, Quang-Tu},
title = {Injectivity radius of manifolds with a {Lie} structure at infinity},
journal = {Annales math\'ematiques Blaise Pascal},
pages = {235--246},
publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
volume = {29},
number = {2},
year = {2022},
doi = {10.5802/ambp.412},
language = {en},
url = {http://www.numdam.org/articles/10.5802/ambp.412/}
}
TY - JOUR AU - Bui, Quang-Tu TI - Injectivity radius of manifolds with a Lie structure at infinity JO - Annales mathématiques Blaise Pascal PY - 2022 SP - 235 EP - 246 VL - 29 IS - 2 PB - Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.412/ DO - 10.5802/ambp.412 LA - en ID - AMBP_2022__29_2_235_0 ER -
%0 Journal Article %A Bui, Quang-Tu %T Injectivity radius of manifolds with a Lie structure at infinity %J Annales mathématiques Blaise Pascal %D 2022 %P 235-246 %V 29 %N 2 %I Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.412/ %R 10.5802/ambp.412 %G en %F AMBP_2022__29_2_235_0
Bui, Quang-Tu. Injectivity radius of manifolds with a Lie structure at infinity. Annales mathématiques Blaise Pascal, Tome 29 (2022) no. 2, pp. 235-246. doi : 10.5802/ambp.412. http://www.numdam.org/articles/10.5802/ambp.412/
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