Foliations by planes and Lie group actions

J. A. Álvarez López; J. L. Arraut; C. Biasi

Annales Polonici Mathematici (2003)

  • Volume: 82, Issue: 1, page 61-69
  • ISSN: 0066-2216

Abstract

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Let N be a closed orientable n-manifold, n ≥ 3, and K a compact non-empty subset. We prove that the existence of a transversally orientable codimension one foliation on N∖K with leaves homeomorphic to ℝ n - 1 , in the relative topology, implies that K must be connected. If in addition one imposes some restrictions on the homology of K, then N must be a homotopy sphere. Next we consider C² actions of a Lie group diffeomorphic to ℝ n - 1 on N and obtain our main result: if K, the set of singular points of the action, is a finite non-empty subset, then K contains only one point and N is homeomorphic to Sⁿ.

How to cite

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J. A. Álvarez López, J. L. Arraut, and C. Biasi. "Foliations by planes and Lie group actions." Annales Polonici Mathematici 82.1 (2003): 61-69. <http://eudml.org/doc/280483>.

@article{J2003,
abstract = {Let N be a closed orientable n-manifold, n ≥ 3, and K a compact non-empty subset. We prove that the existence of a transversally orientable codimension one foliation on N∖K with leaves homeomorphic to $ℝ^\{n-1\}$, in the relative topology, implies that K must be connected. If in addition one imposes some restrictions on the homology of K, then N must be a homotopy sphere. Next we consider C² actions of a Lie group diffeomorphic to $ℝ^\{n-1\}$ on N and obtain our main result: if K, the set of singular points of the action, is a finite non-empty subset, then K contains only one point and N is homeomorphic to Sⁿ.},
author = {J. A. Álvarez López, J. L. Arraut, C. Biasi},
journal = {Annales Polonici Mathematici},
keywords = {foliation by planes; homotopy spheres; actions},
language = {eng},
number = {1},
pages = {61-69},
title = {Foliations by planes and Lie group actions},
url = {http://eudml.org/doc/280483},
volume = {82},
year = {2003},
}

TY - JOUR
AU - J. A. Álvarez López
AU - J. L. Arraut
AU - C. Biasi
TI - Foliations by planes and Lie group actions
JO - Annales Polonici Mathematici
PY - 2003
VL - 82
IS - 1
SP - 61
EP - 69
AB - Let N be a closed orientable n-manifold, n ≥ 3, and K a compact non-empty subset. We prove that the existence of a transversally orientable codimension one foliation on N∖K with leaves homeomorphic to $ℝ^{n-1}$, in the relative topology, implies that K must be connected. If in addition one imposes some restrictions on the homology of K, then N must be a homotopy sphere. Next we consider C² actions of a Lie group diffeomorphic to $ℝ^{n-1}$ on N and obtain our main result: if K, the set of singular points of the action, is a finite non-empty subset, then K contains only one point and N is homeomorphic to Sⁿ.
LA - eng
KW - foliation by planes; homotopy spheres; actions
UR - http://eudml.org/doc/280483
ER -

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