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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Incompressibility of tori transverse to Axiom A flows
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by C. A. Morales PDF
Proc. Amer. Math. Soc. 136 (2008), 4349-4354 Request permission

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
  • MR Author ID: 611238
  • ORCID: 0000-0002-4808-6902
  • Email: morales@impa.br
  • 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
  • © Copyright 2008 American Mathematical Society
  • 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
  • MathSciNet review: 2431049