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On the Proper Homotopy Invariance of the Tucker Property

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Abstract

A non-compact polyhedron P is Tucker if, for any compact subset K ⊂ P, the fundamental group π 1(P − K) is finitely generated. The main result of this note is that a manifold which is proper homotopy equivalent to a Tucker polyhedron is Tucker. We use Poenaru’s theory of the equivalence relations forced by the singularities of a non-degenerate simplicial map.

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Authors and Affiliations

  1. Universitá di Palermo, Dipartimento di Matematica ed Applicazioni, via Archirafi 34, 90123, Palermo, Italy

    Daniele Ettore Otera

  2. Université Paris-Sud, Mathématiques, Bât 425, 91405, Orsay Cedex, France

    Daniele Ettore Otera

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  1. Daniele Ettore Otera
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Correspondence to Daniele Ettore Otera.

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The author is partially supported by GNSAGA of INDAM, by MIUR of Italy (Progetto Giovani Ricercatori) and by Università di Palermo

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Otera, D.E. On the Proper Homotopy Invariance of the Tucker Property. Acta Math Sinica 23, 571–576 (2007). https://doi.org/10.1007/s10114-005-0900-2

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  • DOI: https://doi.org/10.1007/s10114-005-0900-2

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