### 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

Original language | English |
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Pages (from-to) | 571-576 |

Number of pages | 6 |

Journal | Acta Mathematica Sinica |

Volume | 23 |

Publication status | Published - 2007 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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## Cite this

Otera, D. E., & Otera, D. E. (2007). On the proper homotopy invariance of the Tucker property.

*Acta Mathematica Sinica*,*23*, 571-576.