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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 , ) -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 short proof of Eilenberg and Moore’s theorem

Maria Nogin (2007)

Open Mathematics

In this paper we give a short and simple proof the following theorem of S. Eilenberg and J.C. Moore: the only injective object in the category of groups is the trivial group.

A topological version of Bertini's theorem

Artur Piękosz (1995)

Annales Polonici Mathematici

We give a topological version of a Bertini type theorem due to Abhyankar. A new definition of a branched covering is given. If the restriction π V : V Y of the natural projection π: Y × Z → Y to a closed set V ⊂ Y × Z is a branched covering then, under certain assumptions, we can obtain generators of the fundamental group π₁((Y×Z).

Almost-Bieberbach groups with prime order holonomy

Karel Dekimpe, Wim Malfait (1996)

Fundamenta Mathematicae

The main issue of this paper is an attempt to find a decomposition theorem for infra-nilmanifolds in the same spirit as a result of A. Vasquez for flat Riemannian manifolds. That is: we look for infra-nilmanifolds with prime order holonomy which can be obtained as a fiber space with a non-trivial nilmanifold as fiber and an infra-nilmanifold as its base.  In this perspective, we prove the following algebraic result: if E is an almost-Bieberbach group with prime order holonomy,...

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