The extended Schottky space.
The Extended Teichmüller Space.
The geometric quantization of the moduli space of Riemann surfaces with even spin structure.
The geometry of Teichmüller space via geodesic currents.
The geometry of the period mapping on cyclic covers of P1
The mapping class group of a generic quadratic rational map and automorphisms of the 2-shift.
The moduli space of Riemann surfaces is Kähler hyperbolic.
The monodromy groups of Schwarzian equations on closed Riemann surfaces.
The Mumford conjecture
The Mumford Conjecture asserts that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra on the Mumford-Morita-Miller characteristic classes; this can be reformulated in terms of the classifying space derived from the mapping class groups. The conjecture admits a topological generalization, inspired by Tillmann’s theorem that admits an infinite loop space structure after applying Quillen’s plus construction. The text presents the proof by Madsen and...
The outside of the Teichmüller space of punctured tori in Maskit's embedding.
The Picard group of the moduli of higher spin curves.
The Poisson Boundary of the Mapping Class Group and of Teichmüller Space
The Prym vector bundle and Gunning vector bundle over the Teichmüller space.
The space of quasisymmetric mappings.
The sympletic nature of the space of projective connections on Riemann surfaces.
The visual sphere of Teichmüller space and a theorem of Masur-Wolf.
Topological equivalence of metrics in Teichmüller space.
Topological types of symmetries of elliptic-hyperelliptic Riemann surfaces and an application to moduli spaces.
Sea X una superficie de Riemann de género g. Diremos que la superficie X es elíptica-hiperelíptica si admite una involución conforme h de modo que X/〈h〉 tenga género uno. La involución h se llama entonces involución elíptica-hiperelíptica. Si g > 5 entonces la involución h es única, ver [1]. Llamamos simetría a toda involución anticonforme de X. Sea Aut±(X) el grupo de automorfismos conformes y anticonformes de X y σ, τ dos simetrías de X con puntos fijos y tales que {σ, hσ} y {τ, hτ} no...
Topologie de Gromov équivariante, structures hyperboliques et arbres réels.
Trace parameters for Teichmüller space of genus 2 surfaces and mapping class group
We obtain a representation of the mapping class group of genus 2 surface in terms of a coordinate system of the Teichmüller space defined by trace functions.