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Uniform weak* topology and earthquakes in the hyperbolic plane
Author(s) -
Miyachi Hideki,
Šarić Dragomir
Publication year - 2012
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pds026
Subject(s) - mathematics , topology (electrical circuits) , plane (geometry) , geometry , combinatorics
We prove that the bijective correspondence between the space of bounded measured laminations ℳℒ b (ℍ) and the universal Teichmüller space T (ℍ) given byλ ↦ E λ |S 1is a homeomorphism for the uniform weak* topology on ℳℒ b (ℍ) and the Teichmüller topology on T (ℍ), where E λ is an earthquake with an earthquake measure λ. A corollary is that earthquakes with discrete earthquake measures are dense in T (ℍ). We also establish infinitesimal versions of the above results.