On invariant linearization of Lie groupoids

被引：0
作者：
Matias del Hoyo
Mateus de Melo
机构：
[1] Universidade Federal Fluminense (UFF),Instituto de Matemática e Estatística
[2] Universidade de São Paulo (USP),undefined
来源：
Letters in Mathematical Physics | 2021年 / 111卷
关键词：
Lie groupoids; Linearization; Invariant metrics; Differentiable stacks; 22A22; 58H05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The linearization theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization remains somehow open. We address it here, by first giving a counter-example to a previous conjecture, and then proving a sufficient criterion that uses compatible complete metrics and covers the case of proper group actions. We also show a partial converse that fixes and extends previous results in the literature.
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  • [1] Crainic M(2013)On the Linearization Theorem for proper Lie groupoids Ann. Sci. Éc. Norm. Supér. 46 723-746
  • [2] Struchiner I(2013)Lie Groupoids and their orbispaces Port. Math. 70 161-210
  • [3] del Hoyo M(2016)Complete connections on fiber bundles Indag. Math. 27 985-990
  • [4] del Hoyo M(2020)Geodesics on Riemannian stacks Transform. Groups 735 143-173
  • [5] del Hoyo M(2018)Riemannian Metrics on Lie Groupoids J. Reine Angew. Math. 292 103-132
  • [6] de Melo M(2019)Riemannian metrics on differentiable stacks Math. Z. 11 236-242
  • [7] del Hoyo M(1960)A sufficient condition that a mapping of Riemannian manifolds be a fibre bundle Proc. AMS 354 3771-3787
  • [8] Fernandes RL(2002)Submersions, fibrations and bundles Trans. Am. Math. Soc. 371 4931-4949
  • [9] del Hoyo M(2019)A slice theorem for singular Riemannian foliations, with applications Trans. Am. Math. Soc. 694 49-84
  • [10] Fernandes RL(2014)Geometry of orbit spaces of proper Lie groupoids J. Reine Angew. Math. 1 493-511
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