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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 $K_{0} (ℤ [π_{0} {(W H (X))}_{α}^{*}])$ . We prove that every family $w_{α}^{H}$ of elements of the groups $K_{0} (ℤ [π_{0} {(W H (X))}_{α}^{*}])$ 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.

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.

Currently displaying 1 – 17 of 17

Page 1

Displaying 1 – 17 of 17

A complement to the theory of equivariant finiteness obstructions

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

Ends of Maps, II.

Existence of Finitely Dominated CW-Complexes with G1(X) = ... (X) and non-Vanishing Finiteness Obstruction.

G-CW-Surgery and K...(ZG).

Manifolds with non-stable fundamental groups at infinity.

Manifolds with non-stable fundamental groups at infinity, II.

On equivariant finiteness

On the finiteness obstruction of certain periodic groups.

Products of open manifolds with ℝ

Projective and Hilbert modules over group algebras, and finitely dominated spaces.

Semifree Topological Actions of Finite Groups on Spheres.

Steenrod's Equivariant Moore Space Problem for Cohomologically Trivial Modules.

The Picard group of the Burnside ring.

The transfer maps induced in the algebraic K...- and K...-groups by a fibration I.

Wall's obstructions and Whitehead torsion.

Whitehead transfers for S1-bundles, an algebraic description.

Currently displaying 1 – 17 of 17