Hatice Zeybek | Searcharxiv

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↗

arXiv2019

Shearing deformations of Hitchin representations and the Atiyah-Bott-Goldman symplectic form

The Hitchin component Hit_n(S) of a closed surface S is a preferred component of the character variety X_PSL_n(R)(S) consisting of homomorphisms from the fundamental group pi_1(S) to the Lie group PSL_n(R)(S), whose elements enjoy remarkable geometric and dynamical properties. We consider a certain type of deformations of the elements of Hit_n(S), called shearing deformations, and compute their pairing for the Atiyah-Bott-Goldman symplectic form of the character variety.

math.GT↗