A note on open 3-manifolds supporting foliations by planes
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- by Carlos Biasi and Carlos Maquera PDF
- Proc. Amer. Math. Soc. 140 (2012), 961-969 Request permission
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 $\mathcal {F}$ 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 $\mathbb {T}^2\times \mathbb {R}.$ Furthermore, in this case we give a complete description of the foliation.References
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Additional Information
- Carlos Biasi
- Affiliation: Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo-São Carlos, Av. do Trabalhador São-Carlense 400, 13560-970 São Carlos, SP, Brazil
- Email: biasi@icmc.usp.br
- Carlos Maquera
- Affiliation: Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo-São Carlos, Av. do Trabalhador São-Carlense 400, 13560-970 São Carlos, SP, Brazil
- Email: cmaquera@icmc.usp.br
- Received by editor(s): June 15, 2009
- Received by editor(s) in revised form: May 28, 2010, August 28, 2010, and December 18, 2010
- Published electronically: July 18, 2011
- Additional Notes: The first author was supported by FAPESP Grant 2008/57607-6.
The second author was supported by CNPq and FAPESP Grants 2008/57607-6 and 2009/17493-4. - Communicated by: Alexander N. Dranishnikov
- © Copyright 2011 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 140 (2012), 961-969
- MSC (2010): Primary 37C85; Secondary 57R30
- DOI: https://doi.org/10.1090/S0002-9939-2011-10960-2
- MathSciNet review: 2869080