Foliations by planes and Lie group actions

• Autorzy: J. A. Álvarez López , J. L. Arraut , C. Biasi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57S25: Groups acting on specific manifolds
• 57R30: Foliations; geometric theory
• 57R25: Vector fields, frame fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2003
• Tom: 82
• Numer: 1
• Strony: 61-69

Daty

wydano

2003

Twórcy

autor

J. A. Álvarez López

• Departamento de Xeometría e Topoloxía, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain

autor

J. L. Arraut

• Departamento de Matemática, nstituto de Matemática e Computação, Universidade de São Paulo, Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos SP, Brasil

autor

C. Biasi

• Departamento de Matemática, Instituto de Matemática e Computação, Universidade de São Paulo, Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos SP, Brasil

Identyfikatory

DOI

10.4064/ap82-1-7