Teichmüller spaces and HR structures for hyperbolic surface dynamics

Dual Teichmüller and Lamination Spaces

We survey explicit coordinate descriptions for two (A and X) versions of Teichmüller and lamination spaces for open 2D surfaces, and extend them to the more general setup of surfaces with distinguished collections of points on the boundary. Main features, such as mapping class group action, Poisson and symplectic structures and others, are described in these terms. The lamination spaces are int...

Dual Teichmüller Spaces

We describe in elementary geometrical terms Teichmüller spaces of decorated and holed surfaces. We construct explicit global coordinates on them as well as on the spaces of measured laminations with compact and closed support respectively and show explicitly that the latter spaces are asymptotically isomorphic to the former. We discuss briefly quantisation of Teichmüller spaces and some other a...

Canonical Mappings between Teichmüller Spaces

Introduction. In an important survey article [BIO] Bers reported on the state of knowledge of Teichmüller theory. There has been a lot of progress in the field since that time. The purpose of this paper is to summarize the recent work in one area of Teichmüller space theory. We will concentrate on the hyperbolic properties of Teichmüller spaces, and present as many consequences of this hyperbol...

Dynamics over Teichmüller Space

Bounding Surface Actions on Hyperbolic Spaces

We give a diameter bound for fundamental domains for isometric actions of closed hyperbolic surface groups on δ-hyperbolic spaces, where the bound depends on the hyperbolicity constant δ, the genus of the surface, and the injectivity radius of the action, which we assume to be strictly positive.