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On locally Lipschitz locally compact transformation groups of manifolds

A. A. George Michael

Archivum Mathematicum (2007)

  • Volume: 043, Issue: 3, page 159-162
  • ISSN: 0044-8753

Abstract

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In this paper we show that a “locally Lipschitz” locally compact transformation group acting continuously and effectively on a connected paracompact locally Euclidean topological manifold is a Lie group. This is a contribution to the proof of the Hilbert-Smith conjecture. It generalizes the classical Bochner-Montgomery-Kuranishi Theorem[1, 9] and also the Repovš-Ščepin Theorem [17] which holds only for Riemannian manifolds.

How to cite

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George Michael, A. A.. "On locally Lipschitz locally compact transformation groups of manifolds." Archivum Mathematicum 043.3 (2007): 159-162. <http://eudml.org/doc/250154>.

@article{GeorgeMichael2007,
abstract = {In this paper we show that a “locally Lipschitz” locally compact transformation group acting continuously and effectively on a connected paracompact locally Euclidean topological manifold is a Lie group. This is a contribution to the proof of the Hilbert-Smith conjecture. It generalizes the classical Bochner-Montgomery-Kuranishi Theorem[1, 9] and also the Repovš-Ščepin Theorem [17] which holds only for Riemannian manifolds.},
author = {George Michael, A. A.},
journal = {Archivum Mathematicum},
keywords = {locally Lipschitz transformation group; Hilbert-Smith conjecture; locally Lipschitz transformation group; Hilbert-Smith conjecture},
language = {eng},
number = {3},
pages = {159-162},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On locally Lipschitz locally compact transformation groups of manifolds},
url = {http://eudml.org/doc/250154},
volume = {043},
year = {2007},
}

TY - JOUR
AU - George Michael, A. A.
TI - On locally Lipschitz locally compact transformation groups of manifolds
JO - Archivum Mathematicum
PY - 2007
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 043
IS - 3
SP - 159
EP - 162
AB - In this paper we show that a “locally Lipschitz” locally compact transformation group acting continuously and effectively on a connected paracompact locally Euclidean topological manifold is a Lie group. This is a contribution to the proof of the Hilbert-Smith conjecture. It generalizes the classical Bochner-Montgomery-Kuranishi Theorem[1, 9] and also the Repovš-Ščepin Theorem [17] which holds only for Riemannian manifolds.
LA - eng
KW - locally Lipschitz transformation group; Hilbert-Smith conjecture; locally Lipschitz transformation group; Hilbert-Smith conjecture
UR - http://eudml.org/doc/250154
ER -

References

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