Article Dans Une Revue Mathematical Proceedings of the Cambridge Philosophical Society Année : 2007

On the topology defined by Thurston's asymmetric metric

Résumé

In this paper, we establish some properties of Thurston's asymmetric metric L on the Teichmueller space T of a surface with negative Euler characteristic. We study convergence of sequences of elements in T in the sense of L, as well as sequences that tend to infinity in T. We show that the topology that the asymmetric metric induces on Teichmueller 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.

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hal-00129728 , version 1 (08-02-2007)

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Athanase Papadopoulos, Guillaume Théret. On the topology defined by Thurston's asymmetric metric. Mathematical Proceedings of the Cambridge Philosophical Society, 2007, 142 (3), pp.487-496. ⟨10.1017/S0305004107000023⟩. ⟨hal-00129728⟩
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