Foliations by planes and Lie group actions

  1. López, J. A. Álvarez 1234
  2. Arraut, J. L. 57891011
  3. Biasi, C. 5678910
  1. 1 Departamento de Xeometría e Topoloxía
  2. 2 Facultade de Matemáticas
  3. 3 Universidade de Santiago de Compostela
    info

    Universidade de Santiago de Compostela

    Santiago de Compostela, España

    ROR https://ror.org/030eybx10

  4. 4 15706 Santiago de Compostela, Spain
  5. 5 Departamento de Matemática
  6. 6 Instituto de Matemática e Computação
  7. 7 Universidade de São Paulo
    info

    Universidade de São Paulo

    São Paulo, Brasil

    ROR https://ror.org/036rp1748

  8. 8 Campus de São Carlos
  9. 9 Caixa Postal 668
  10. 10 13560-970 São Carlos SP, Brasil
  11. 11 nstituto de Matemática e Computação
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Revista:
Annales Polonici Mathematici

ISSN: 0066-2216,  1730-6272

Ano de publicación: 2003

Volume: 82

Número: 1

Páxinas: 61-69

Tipo: Artigo

DOI: 10.4064/AP82-1-7 GOOGLE SCHOLAR lock_openAcceso aberto editor

Outras publicacións en: Annales Polonici Mathematici

Resumo

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 Rn−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 Rn−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.