Topological conjugacy of locally free ${\bf R}^{n-1}$ actions on $n$-manifolds

Tischler, David C.; Tischler, Rosamond W.

doi:10.5802/aif.539

Topological conjugacy of locally free

𝐑^{n - 1}

actions on

n

-manifolds

Tischler, David C. ; Tischler, Rosamond W.

Annales de l'Institut Fourier, Tome 24 (1974) no. 4, pp. 213-227

Abstract (VO)
Résumé

For actions as in the title we associate a collection of rotation numbers. If one of them is sufficiently irrational then the action is conjugate (as an action) to either a linear action on a torus or to an action on a principal $T^{k}$ bundle over $T^{2}$ with $T^{k} \times R^{1}$ orbits.

À une action au sens du titre, nous attachons une collection des nombres de rotation. Si l’un des nombres est suffisamment irrationnel, alors l’action est conjuguée (au sens d’une action) soit à une action linéaire sur un tore, soit à une action sur un fibré principal sur $T^{2}$ de fibre $T^{k}$ avec les orbites isomorphes à $T^{k} \times R^{1}$ .

MR Zbl

DOI : 10.5802/aif.539

@article{AIF_1974__24_4_213_0,
     author = {Tischler, David C. and Tischler, Rosamond W.},
     title = {Topological conjugacy of locally free ${\bf R}^{n-1}$ actions on $n$-manifolds},
     journal = {Annales de l'Institut Fourier},
     pages = {213--227},
     year = {1974},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {24},
     number = {4},
     doi = {10.5802/aif.539},
     mrnumber = {52 #1726},
     zbl = {0287.57016},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/aif.539/}
}

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Tischler, David C.; Tischler, Rosamond W. Topological conjugacy of locally free ${\bf R}^{n-1}$ actions on $n$-manifolds. Annales de l'Institut Fourier, Tome 24 (1974) no. 4, pp. 213-227. doi: 10.5802/aif.539

Bibliographie
Cité par

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[3] R. Tischler, Thesis, " Conjugacy Problems for Rk Actions ", City University of New York, 1971.

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[5] A. Wintner, The Linear Difference Equation of First Order for Angular Variables, Duke Mathematics Journal, 12 (1945), 445-449. | Zbl | MR

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