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Non abelian Reidemeister torsion and volume form on the SU(2)-representation space of knot groups

Jérôme Dubois (2005)

Annales de l’institut Fourier

For a knot K in the 3-sphere and a regular representation of its group G K into SU(2) we construct a non abelian Reidemeister torsion form on the first twisted cohomology group of the knot exterior. This non abelian Reidemeister torsion form provides a volume form on the SU(2)-representation space of G K . In another way, we construct using Casson’s original construction a natural volume form on the SU(2)-representation space of G K . Next, we compare these two apparently different points of view on the representation...

On a volume element of a Hitchin component

Yaşar Sözen (2012)

Fundamenta Mathematicae

Let Σ be a closed oriented Riemann surface of genus at least 2. By using symplectic chain complex, we construct a volume element for a Hitchin component of Hom(π₁(Σ),PSLₙ(ℝ))/PSLₙ(ℝ) for n > 2.

On deformations of spherical isometric foldings

Ana M. Breda, Altino F. Santos (2010)

Czechoslovak Mathematical Journal

The behavior of special classes of isometric foldings of the Riemannian sphere S 2 under the action of angular conformal deformations is considered. It is shown that within these classes any isometric folding is continuously deformable into the standard spherical isometric folding f s defined by f s ( x , y , z ) = ( x , y , | z | ) .

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