Lie groupoids of symmetries and geometric structures on manifolds
Invariant manifolds and limit periodic sets of discontinuous foliations
Systems of transversal sections for 3-dimensional Reeb flows
| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Sao Paulo, Inst Ciencia Matemat & Comp, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | Proceedings of the American Mathematical Society; v. 140, n. 3, p. 961-969, MAR 2012. |
| Web of Science Citations: | 0 |
| Abstract | |
We show that if N, an open connected n-manifold with finitely generated fundamental group, is C-2 foliated by closed planes, then pi(1)(N) is a free group. This implies that if pi(1)(N) has an abelian subgroup of rank greater than one, then F has at least a nonclosed leaf. Next, we show that if N is three dimensional with fundamental group abelian of rank greater than one, then N is homeomorphic to T-2 x R. Furthermore, in this case we give a complete description of the foliation. (AU) | |
| FAPESP's process: | 09/17493-4 - Dynamical systems defined by actions of Rk |
| Grantee: | Carlos Alberto Maquera Apaza |
| Support Opportunities: | Regular Research Grants |