Parametrizations of some Teichmüller spaces by trace functions (Q2841087)

The paper under review gives elegant explicit parameterizations of low-dimensional Teichmüller spaces for the twice-punctured torus (\(T_{1, 2}\)) and compact genus 2 surfaces (\(T_{2,0}\)), via trace functions on the representation varieties of the fundamental group of the surface into \(\mathrm{PSL}(2, \mathbb R)\) (equivalently via geodesic length functions). The authors also give an explicit description of a rational representation of the mapping class group action in these coordinates.