Topological conjugacy of locally free 𝐑 n - 1 actions on n -manifolds

David C. Tischler; Rosamond W. Tischler

Annales de l'institut Fourier (1974)

  • Volume: 24, Issue: 4, page 213-227
  • ISSN: 0373-0956

Abstract

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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 × R 1 orbits.

How to cite

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Tischler, David C., and Tischler, Rosamond W.. "Topological conjugacy of locally free ${\bf R}^{n-1}$ actions on $n$-manifolds." Annales de l'institut Fourier 24.4 (1974): 213-227. <http://eudml.org/doc/74200>.

@article{Tischler1974,
abstract = {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.},
author = {Tischler, David C., Tischler, Rosamond W.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {4},
pages = {213-227},
publisher = {Association des Annales de l'Institut Fourier},
title = {Topological conjugacy of locally free $\{\bf R\}^\{n-1\}$ actions on $n$-manifolds},
url = {http://eudml.org/doc/74200},
volume = {24},
year = {1974},
}

TY - JOUR
AU - Tischler, David C.
AU - Tischler, Rosamond W.
TI - Topological conjugacy of locally free ${\bf R}^{n-1}$ actions on $n$-manifolds
JO - Annales de l'institut Fourier
PY - 1974
PB - Association des Annales de l'Institut Fourier
VL - 24
IS - 4
SP - 213
EP - 227
AB - 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.
LA - eng
UR - http://eudml.org/doc/74200
ER -

References

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  1. [1] R. SACKSTEDER, Foliations and Pseudogroups, American Journal of Mathematics, 87 (1965), 98-102. Zbl0136.20903MR30 #4268
  2. [2] S. STERNBERG, Celestial Mechanics, Part II, W. A. Benjamin, New York, 1969. Zbl0194.56702
  3. [3] R. TISCHLER, Thesis, " Conjugacy Problems for Rk Actions ", City University of New York, 1971. 
  4. [4] Y. KATZNELSON, An Introduction to Harmonic Analysis, John Wiley and Sons, New York, 1968. Zbl0169.17902MR40 #1734
  5. [5] A. WINTNER, The Linear Difference Equation of First Order for Angular Variables, Duke Mathematics Journal, 12 (1945), 445-449. Zbl0061.20005MR7,163c

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