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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.

A relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion

Yoshikazu Yamaguchi (2008)

Annales de l’institut Fourier

We show a relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion for a $λ$ -regular $SU (2)$ or $SL (2, ℂ)$ -representation of a knot group. Then we give a method to calculate the non-acyclic Reidemeister torsion of a knot exterior. We calculate a new example and investigate the behavior of the non-acyclic Reidemeister torsion associated to a $2$ -bridge knot and $SU (2)$ -representations of its knot group.

A Semigroup of Simple Homotopy Types.

Allan J. Sieradski (1977)

Mathematische Zeitschrift

A Splitting Theorem for Manifolds.

Sylvain E. Cappell (1976)

Inventiones mathematicae

A topological collapse number for all spaces

P. Doyle (1975)

Fundamenta Mathematicae

Algebraic properties of decorated splitting obstruction groups

A. Cavicchioli, Y. V. Muranov, D. Repovš (2001)

Bollettino dell'Unione Matematica Italiana

In questo articolo si riassumono le definizioni e le principali proprietà dei gruppi di ostruzione con decorazione di tipo LS e LP. Si stabiliscono nuove relazioni fra questi gruppi e si descrivono le proprietà delle mappe naturali fra differenti gruppi con decorazione. Si costruiscono varie successioni spettrali, contenenti questi gruppi con decorazione, e si studiano la loro connessione con le successioni spettrali in $K$ -teoria per certe estensioni quadratiche di antistrutture. Infine, si introduce...

Algebraic Torsion for Infinite Simple Homotopy Types

J.B. Wagoner, F.T. Farrell (1972)

Commentarii mathematici Helvetici

An Algebraic Model for G-Simple Homotopy Types.

Mel Rothenberg, Triantafillou Georgia (1984)

Mathematische Annalen

An introduction to the abelian Reidemeister torsion of three-dimensional manifolds

Gwénaël Massuyeau (2011)

Annales mathématiques Blaise Pascal

These notes accompany some lectures given at the autumn school “Tresses in Pau” in October 2009. The abelian Reidemeister torsion for $3$ -manifolds, and its refinements by Turaev, are introduced. Some applications, including relations between the Reidemeister torsion and other classical invariants, are surveyed.

Analytic and Reidemeister Torsion for Representation in Finite Type Hilbert Modules.

D. Burghelea, L. Friedlander (1996)

Geometric and functional analysis

Äquivariante Whiteheadtorsion.

Henning Hausschild (1978/1979)

Manuscripta mathematica

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