Geodesic
Canonical stratification of definable Lie groupoids
Journal of Singularities, Tome 26 (2023), pp. 63-75

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Our aim is to precisely present a tame topology counterpart to canonical stratification of a Lie groupoid. We consider a definable Lie groupoid in semialgebraic, subanalytic, o-minimal over R, or more generally, Shiota's X-category. We show that there exists a canonical Whitney stratification of the Lie groupoid into definable strata which are invariant under the groupoid action. This is a generalization and refinement of results on real algebraic group action which J. N. Mather and V. A. Vassiliev independently stated with sketchy proofs. A crucial change to their proofs is to use Shiota's isotopy lemma and approximation theorem in the context of tame topology.
DOI : 10.5427/jsing.2023.26d
Classification : 14P10, 32B20 
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     author = {Masato Tanabe},
     title = {Canonical stratification of definable {Lie} groupoids},
     journal = {Journal of Singularities},
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     year = {2023},
     doi = {10.5427/jsing.2023.26d},
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Masato Tanabe. Canonical stratification of definable Lie groupoids. Journal of Singularities, Tome 26 (2023), pp. 63-75. doi: 10.5427/jsing.2023.26d

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