arXiv subjects

Yasar Sozen

Publications and source records attributed to Yasar Sozen.

3 recordsLinked to original sources

arXiv2021

A note on Reidemeister Torsion of G-Anosov Representations

This article considers $G$-Anosov representations of a fixed closed oriented Riemann surface $Σ$ of genus at least $2$. Here, $G$ is the Lie group $\text{PSp}(2n,\mathbb{R}$), $\text{PSO}(n,n)$ or $\text{PSO}(n,n+1)$. It proves that Reidemeister torsion (R-torsion) associated to $Σ$ with coefficients in the adjoint bundle representations of such representations is well-defined. Moreover, by using symplectic chain complex method, it establishes a novel formula for R-torsion of such representations in terms of the Atiyah-Bott-Goldman symplectic form corresponding to the Lie group $G$. Furtermore, it applies the results to Hitchin components, in particular, Teichmüller space.

math.GT↗

arXiv2004

Reidemeister torsion of a symplcetic complex

We consider a claim mentioned in \cite{Witten} pp 187 about the relation between a symplectic chain complex with $ω-$compatible bases and Reidemeister Torsion of it. This is an explanation of it.

math.GT↗

arXiv2002

Variation of the Liouville measure of a hyperbolic surface

For a compact riemannian manifold of negative curvature, the geodesic foliation of its unit tangent bundle is independent of the negatively curved metric, up to Holder bicontinuous homeomorphism. However, the riemannian metric defines a natural transverse measure to this foliation, the Liouville transverse measure, which does depend on the metric. For a surface S, we show that the map which to a hyperbolic metric on S associates its Liouville transverse measure is differentiable, in an appropriate sense. Its tangent map is valued in the space of transverse Holder distributions for the geodesic foliation.

math.DS↗