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A complement to the theory of equivariant finiteness obstructions

Paweł Andrzejewski (1996)

Fundamenta Mathematicae

It is known ([1], [2]) that a construction of equivariant finiteness obstructions leads to a family w α H ( X ) of elements of the groups K 0 ( [ π 0 ( W H ( X ) ) α * ] ) . We prove that every family w α H of elements of the groups K 0 ( [ π 0 ( W H ( X ) ) α * ] ) can be realized as the family of equivariant finiteness obstructions w α H ( X ) of an appropriate finitely dominated G-complex X. As an application of this result we show the natural equivalence of the geometric construction of equivariant finiteness obstruction ([5], [6]) and equivariant generalization of Wall’s obstruction...

A non-𝒵-compactifiable polyhedron whose product with the Hilbert cube is 𝒵-compactifiable

C. R. Guilbault (2001)

Fundamenta Mathematicae

We construct a locally compact 2-dimensional polyhedron X which does not admit a 𝒵-compactification, but which becomes 𝒵-compactifiable upon crossing with the Hilbert cube. This answers a long-standing question posed by Chapman and Siebenmann in 1976 and repeated in the 1976, 1979 and 1990 versions of Open Problems in Infinite-Dimensional Topology. Our solution corrects an error in the 1990 problem list.

Products of open manifolds with ℝ

Craig R. Guilbault (2007)

Fundamenta Mathematicae

We present a characterization of those open n-manifolds (n ≥ 5) whose products with the real line are homeomorphic to interiors of compact (n+1)-manifolds with boundary.

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