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Manifolds with S 1-category 2 have cyclic fundamental groups

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Abstract

A closed topological n-manifold M n is of S 1-category 2 if it can be covered by two open subsets W 1, W 2 such that the inclusions W i → M n factor homotopically through maps W i → S 1. We show that for n > 3 the fundamental group of such an n-manifold is either trivial or infinite cyclic.

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Authors and Affiliations

  1. Centro de Investigación en Matemáticas, A.P. 402, 36000, Guanajuato, Gto, Mexico

    J. C. Gómez-Larrañaga & F. González-Acuña

  2. Instituto de Matemáticas, UNAM, Ciudad Universitaria, 04510, Mexico, D.F., Mexico

    F. González-Acuña

  3. Department of Mathematics, Florida State University, Tallahasee, FL, 32306, USA

    Wolfgang Heil

Authors
  1. J. C. Gómez-Larrañaga
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  2. F. González-Acuña
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  3. Wolfgang Heil
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Correspondence to Wolfgang Heil.

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Dedicated to José María Montesinos on the occasion of his 65th birthday.

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Gómez-Larrañaga, J.C., González-Acuña, F. & Heil, W. Manifolds with S 1-category 2 have cyclic fundamental groups. Math. Z. 266, 783–788 (2010). https://doi.org/10.1007/s00209-009-0598-4

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  • DOI: https://doi.org/10.1007/s00209-009-0598-4

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