Classical Teichmuller theory and (2+1) gravity

TL;DR

This paper explores the connection between classical Teichmuller theory, geodesic flows, and (2+1) dimensional gravity, providing a geometric framework for understanding particle evolution in complex topologies.

Contribution

It introduces a novel geometric approach linking Teichmuller theory with (2+1) gravity, including explicit spacetime constructions and phase space analysis.

Findings

Canonical description of gravity systems via Teichmuller geodesic flows

Explicit York's slicing for associated spacetimes

Interpretation of asymptotic states through measured foliations

Abstract

We consider classical Teichmuller theory and the geodesic flow on the cotangent bundle of the Teichmuller space. We show that the corresponding orbits provide a canonical description of certain (2+1) gravity systems in which a set of point-like particles evolve in universes with topology S_g x R where S_g is a Riemann surface of genus g >1. We construct an explicit York's slicing presentation of the associated spacetimes, we give an interpretation of the asymptotic states in terms of measured foliations and discuss the structure of the phase spaces.