Abstract
In [3] Paul S. Mostert classifies all topological actions of compact connected Lie groups on connected (n + l)-dimensional manifolds which have n-dimensional orbits. If one starts from the assumption of differentiability a classification is very much easier, but our results show that the list given by Mostert (loc. cit.) for the compact case with n = 2 has some omissions. In this note we therefore give a completed list for this case, and a brief indication of how it may be obtained when the simplifying assumption of differentiability is made.
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References
Jänich,K.: Differenzierbare Mannigfaltigkeiten mit Rand als Orbiträume differenzierbarer G-Mannigfaltigkeiten ohne Rand, Topology 5, 301–320 (1966).
Milnor,J.: Whitehead torsion, Bull. Amer. Math. Soc. 72, 358–426 (1966).
Mostert,P. S.: On a compact Lie group acting on a manifold, Ann. Math. 65, 447–455
Mostert,P. S.: On a compact Lie group acting on a manifold, (1957); Errata, Ann. Math. 66, 589 (1957).
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Neumann, W.D. (1968). 3-Dimensional G-Manifolds with 2-Dimensional Orbits. In: Mostert, P.S. (eds) Proceedings of the Conference on Transformation Groups. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46141-5_16
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DOI: https://doi.org/10.1007/978-3-642-46141-5_16
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