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
OTERA DE (2007). On the proper homotopy invariance of the Tucker property. ACTA MATHEMATICA SINICA, 23(3), 571-576 [10.1007/s10114-005-0900-2].
On the proper homotopy invariance of the Tucker property
OTERA, Daniele Ettore
2007-01-01
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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