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Incompressibility of tori transverse to Axiom A flows


Author: C. A. Morales
Journal: Proc. Amer. Math. Soc. 136 (2008), 4349-4354
MSC (2000): Primary 37D20; Secondary 57M27
DOI: https://doi.org/10.1090/S0002-9939-08-09409-4
Published electronically: June 25, 2008
MathSciNet review: 2431049
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Abstract: We prove that a torus transverse to an Axiom A vector field that does not exhibit sinks, sources or null homotopic periodic orbits on a closed irreducible $ 3$-manifold is incompressible. This strengthens the works of Brunella (1993), Fenley (1995), and Mosher (1992).


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Additional Information

C. A. Morales
Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, P. O. Box 68530, 21945-970 Rio de Janeiro, Brazil
Email: morales@impa.br

DOI: https://doi.org/10.1090/S0002-9939-08-09409-4
Keywords: Sink, vector field, atoroidal, incompressible torus
Received by editor(s): May 22, 2007
Received by editor(s) in revised form: October 3, 2007, and October 24, 2007
Published electronically: June 25, 2008
Additional Notes: This work was supported in part by CNPq, FAPERJ and PRONEX-Brazil. The author thanks Professors E. Apaza, D. Carrasco-Olivera and B. San Martin for helpful conversations. He also thanks the Instituto de Matemáticas Puras e Aplicadas (IMPA) for its kind hospitality.
Communicated by: Jane M. Hawkins
Article copyright: © Copyright 2008 American Mathematical Society

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