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We define an isotopy invariant of embeddings $N \to ℝ^{m}$ of manifolds into Euclidean space. This invariant together with the α-invariant of Haefliger-Wu is complete in the dimension range where the α-invariant could be incomplete. We also define parametric connected sum of certain embeddings (analogous to surgery). This allows us to obtain new completeness results for the α-invariant and the following estimation of isotopy classes of embeddings. In the piecewise-linear category, for a (3n-2m+2)-connected...

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.

A Note on Higher Dimensional Knots.

G. Ananda Swarup (1971)

Mathematische Zeitschrift

A Quick proof of Singhof's cat (M x S1) = cat (M) + 1 theorem.

Luis Montejano (1983)

Manuscripta mathematica

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.