Closed Teichmueller geodesics in the thin part of moduli space

A cofinite universal space for proper actions for mapping class groups

We prove that the mapping class group $Γ_{g,n}$ for surfaces of negative Euler characteristic has a cofinite universal space $\E$ for proper actions (the resulting quotient is a finite $CW$-complex). The approach is to construct a truncated Teichmueller space $\T_{g,n}(ε)$ by introducing a lower bound for the length of shortest closed geodesics and showing that $\T_{g,n}(ε)$ is a $Γ_{g,n}$ equivariant deformation retract of the Teichmueller space $\T_{g, n}$. The existence of such a cofinite universal space is important in the study of the cohomology of the group $\gag$. As an application, we …

黎曼曲面模空间中全测地子簇的几何

The geometry of totally geodesic subvarieties of moduli spaces of Riemann surfaces

该论文证明了黎曼曲面模空间中全测地子簇边界的半单性，并据此证明了相关Teichmüller子流形和轨道基本群是层次双曲的，为这些对象提供了新工具。

A dense geodesic ray in the $Out(F_r)$-quotient of reduced Outer Space

In 1981 Masur proved the existence of a dense geodesic in the moduli space for a Teichmüller space. We prove an analogue theorem for reduced Outer Space endowed with the Lipschitz metric. We also prove two results possibly of independent interest: we show Brun's unordered algorithm weakly converges and from this prove that the set of Perron-Frobenius eigenvectors of positive integer $m \times m$ matrices is dense in the positive cone $\mathbb{R}^m_+$ (these matrices will in fact be the transition matrices of positive automorphisms). We give a proof in the appendix that not every point in the b…