Orbit Structure of certain ℝ 2 -actions on solid torus

C. Maquera[1]; L. F. Martins[2]

  • [1] Departamento de Matemática, USP – Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, Caixa Postal 668, CEP 13560-970, São Carlos, SP, Brazil. Work supported by FAPESP of Brazil Grant 02/09425-0.
  • [2] Departamento de Matemática, UNESP – Universidade Estadual Paulista, Instituto de Biologia, Letras e Ciências Exatas, R. Cristóvão Colombo, 2265, Jardim Nazareth, 15054-000, São José do Rio Preto, SP, Brazil. Work supported by FAPESP of Brazil Grant 98/13400-5

Annales de la faculté des sciences de Toulouse Mathématiques (2008)

  • Volume: 17, Issue: 3, page 613-633
  • ISSN: 0240-2963

Abstract

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In this paper we describe the orbit structure of   C 2 -actions of   ℝ 2   on the solid torus   S 1 × D 2   having   S 1 × { 0 }   and   S 1 × ∂ D 2   as the only compact orbits, and   S 1 × { 0 }   as singular set.

How to cite

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Maquera, C., and Martins, L. F.. "Orbit Structure of certain ${\mathbb{R}}^{2}$-actions on solid torus." Annales de la faculté des sciences de Toulouse Mathématiques 17.3 (2008): 613-633. <http://eudml.org/doc/10098>.

@article{Maquera2008,
abstract = {In this paper we describe the orbit structure of  $C^\{2\}$-actions of  $\{\mathbb\{R\}\}^2$  on the solid torus  $S^\{1\}\times D^\{2\}$  having  $S^\{1\} \times \lbrace 0\rbrace $  and  $S^\{1\} \times \partial D^\{2\}$  as the only compact orbits, and  $S^\{1\} \times \lbrace 0 \rbrace $  as singular set.},
affiliation = {Departamento de Matemática, USP – Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, Caixa Postal 668, CEP 13560-970, São Carlos, SP, Brazil. Work supported by FAPESP of Brazil Grant 02/09425-0.; Departamento de Matemática, UNESP – Universidade Estadual Paulista, Instituto de Biologia, Letras e Ciências Exatas, R. Cristóvão Colombo, 2265, Jardim Nazareth, 15054-000, São José do Rio Preto, SP, Brazil. Work supported by FAPESP of Brazil Grant 98/13400-5},
author = {Maquera, C., Martins, L. F.},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {foliation; action; orbit; manifold},
language = {eng},
month = {6},
number = {3},
pages = {613-633},
publisher = {Université Paul Sabatier, Toulouse},
title = {Orbit Structure of certain $\{\mathbb\{R\}\}^\{2\}$-actions on solid torus},
url = {http://eudml.org/doc/10098},
volume = {17},
year = {2008},
}

TY - JOUR
AU - Maquera, C.
AU - Martins, L. F.
TI - Orbit Structure of certain ${\mathbb{R}}^{2}$-actions on solid torus
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2008/6//
PB - Université Paul Sabatier, Toulouse
VL - 17
IS - 3
SP - 613
EP - 633
AB - In this paper we describe the orbit structure of  $C^{2}$-actions of  ${\mathbb{R}}^2$  on the solid torus  $S^{1}\times D^{2}$  having  $S^{1} \times \lbrace 0\rbrace $  and  $S^{1} \times \partial D^{2}$  as the only compact orbits, and  $S^{1} \times \lbrace 0 \rbrace $  as singular set.
LA - eng
KW - foliation; action; orbit; manifold
UR - http://eudml.org/doc/10098
ER -

References

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  10. Rosenberg (H.), Roussarie (R.), Weil (D.).— A classification of closed orientable manifolds of rank two. Ann. of Math., 91, p. 449-464 (1970). Zbl0195.25404MR270391
  11. Sacksteder (R.).— Foliations, pseudogroups. Amer. J. Math., 87, p. 79-102 (1965). Zbl0136.20903MR174061
  12. Scardua (B.), Seade (J.).— Codimension one foliations with Bott-Morse singularities I. Pre-print (2007). 
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