Le rang de certaines variétés closes

Maurice Garançon

Annales de l'institut Fourier (1970)

  • Volume: 20, Issue: 1, page 1-19
  • ISSN: 0373-0956

Abstract

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Let M be a closed and connected n -manifold with a locally free action φ of R n - 1 on M , we prove : if π 1 ( M ) has no element of finite order the inclusion of a leaf of φ into M induces a monomorphism between the fundamentals groups.As an application we prove that the rank of S 3 × T n - 3 is n - 2 .

How to cite

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Garançon, Maurice. "Le rang de certaines variétés closes." Annales de l'institut Fourier 20.1 (1970): 1-19. <http://eudml.org/doc/74001>.

@article{Garançon1970,
abstract = {Soit $M$ une $n$-variété close et connexe munie d’une action localement libre $\varphi $ de $\{\bf R\}^\{n-1\}$ sur $M$, on démontre : si $\pi _1(M)$ ne contient pas d’éléments d’ordre fini, l’inclusion de toute feuille de $\varphi $ dans $M$ induit un monomorphisme des groupes fondamentaux.Comme application on prouve que le rang de $S^3\times T^\{n-3\}$ est $n-2$.},
author = {Garançon, Maurice},
journal = {Annales de l'institut Fourier},
keywords = {topology},
language = {fre},
number = {1},
pages = {1-19},
publisher = {Association des Annales de l'Institut Fourier},
title = {Le rang de certaines variétés closes},
url = {http://eudml.org/doc/74001},
volume = {20},
year = {1970},
}

TY - JOUR
AU - Garançon, Maurice
TI - Le rang de certaines variétés closes
JO - Annales de l'institut Fourier
PY - 1970
PB - Association des Annales de l'Institut Fourier
VL - 20
IS - 1
SP - 1
EP - 19
AB - Soit $M$ une $n$-variété close et connexe munie d’une action localement libre $\varphi $ de ${\bf R}^{n-1}$ sur $M$, on démontre : si $\pi _1(M)$ ne contient pas d’éléments d’ordre fini, l’inclusion de toute feuille de $\varphi $ dans $M$ induit un monomorphisme des groupes fondamentaux.Comme application on prouve que le rang de $S^3\times T^{n-3}$ est $n-2$.
LA - fre
KW - topology
UR - http://eudml.org/doc/74001
ER -

References

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  1. [1] E. LIMA, “Commuting vector fields on S3”, Annals of Math. 8, (1965). Zbl0137.17801MR30 #1517
  2. [2] E. LIMA, Common singularities of commuting vector fields on 2-manifolds, Comment. Math. Helv. 39 (1964), 97-110. Zbl0124.16101MR31 #731
  3. [3] S.P. NOVIKOV, 1) “The Topology Summer inst. Seattle 1963”. Russiom Math. Surveys, vol. 20 (1965). Zbl0125.39804MR33 #716
  4. 2) “Topology of Foliations”, Trudy mosk. math. Obshlch 14, n° 513.83. 
  5. [4] H. ROSENBERG, “Action of Rn on manifolds” Comm. Math. Helvetici vol. 41 (3) (1966-1967). Zbl0145.20301MR34 #6794
  6. [5] H. ROSENBERG, “Rank of S2 x S1” American J. of Math., vol. 87 (1965). Zbl0132.19803MR31 #764
  7. [6] H. ROSENBERG, “Foliations by planes” Topology, vol. 7 (1968). Zbl0157.30504MR37 #3595
  8. [7] H. ROSENBERG, “Singularities of R2 actions” Topology, vol. 7 (1968). Zbl0157.30601MR37 #3596
  9. [8] R. THOM, “Un lemme sur les applications différentiables”. Bol. Soc. Math. Mex. (2) (1956) 59-71. Zbl0075.32201MR21 #910

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