Dynamical zeta functions for geodesic flows and the higher-dimensional Reidemeister torsion for Fuchsian groups

The asymptotic behavior of the Reidemeister torsion for Seifert manifolds and PSL(2;R)-representations of Fuchsian groups

We show that a PSL(2;R)-representation of a Fuchsian group induces the asymptotics of the Reidemeister torsion for the Seifert manifold corresponding to the euler class of the PSL(2;R)-representation. We also show that the limit of leading coefficient of the Reidemeister torsion is determined by the euler class of a PSL(2;R)-representation of a Fuchsian group. In particular, the leading coefficient of the Reidemeister torsion for the unit tangent bundle over a two-orbifold converges to $-χ\log2$ where $χ$ is the Euler characteristic of the two-orbifold. We also give a relation between $\mathbb…

紧致双曲轨道曲面上的扭曲 Ruelle zeta 函数与 Reidemeister-Turaev 挠率

The twisted Ruelle zeta function on compact hyperbolic orbisurfaces and Reidemeister-Turaev torsion

该文研究紧致双曲轨道曲面上扭曲 Ruelle zeta 函数在零点取值与 Reidemeister-Turaev 挠率的关系，推广 Fried 猜想至非酉表示并解决相位符号问题，同时计算消失阶与首项系数。

Analytic torsion versus Reidemeister torsion on hyperbolic 3-manifolds with cusps

For a non-compact hyperbolic 3-manifold with cusps we prove an explicit formula that relates the regularized analytic torsion associated to the even symmetric powers of the standard representation of SL_2(C) to the corresponding Reidemeister torsion. Our proof rests on an expression of the analytic torsion in terms of special values of Ruelle zeta functions as well as on recent work of Pere Menal-Ferrer and Joan Porti.

Non-commutative Reidemeister torsion and Morse-Novikov theory

Given a circle-valued Morse function of a closed oriented manifold, we prove that Reidemeister torsion over a non-commutative formal Laurent polynomial ring equals the product of a certain non-commutative Lefschetz-type zeta function and the algebraic torsion of the Novikov complex over the ring. This paper gives a generalization of the result of Hutchings and Lee on abelian coefficients to the case of skew fields. As a consequence we obtain a Morse theoretical and dynamical description of the higher-order Reidemeister torsion.

耗散 Anosov 流在零处的共振形式

Resonant forms at zero for dissipative Anosov flows

本文研究 $3$-流形上耗散 Anosov 流在零处的共振微分形式，引入 helicity 概念并提供包含 horocyclic 不变性的理论，同时计算了 quasi-Fuchsian flows 等实例的共振 $1$-形式及 Ruelle zeta 函数的消失阶数。

接触 Anosov 流的动力学挠率

Dynamical torsion for contact Anosov flows

本文引入“动力学挠率”这一新对象，证明其与 Turaev 挠率的比值在非循环表示空间上局部常数，并将 Fried 猜想从双曲 3-流形扩展至任意奇数维双曲流形。