Resumen de On the topology defined by Thurston's asymmetric metric

Athanase Papadopoulos , Guillaume Théret

• We establish some properties of Thurston's asymmetric metric L on the Teichmüller space of a surface of genus with punctures and with negative Euler characteristic. We study convergence of sequences of elements in in the sense of L, as well as sequences that tend to infinity in . We show that the topology that the asymmetric metric L induces on Teichmüller space is the same as the usual topology. Furthermore, we show that L satisfies the axioms of a (not necessarily symmetric) metric in the sense of Busemann and conclude that L is complete in the sense of Busemann.