The Teichmüller distance between finite index subgroups of PSL2(Z)
Markovic, V. (Vladimir) and Šarić, Dragomir. (2008) The Teichmüller distance between finite index subgroups of PSL2(Z). Geometriae Dedicata, Vol.136 (No.1). pp. 145-165. ISSN 0046-5755Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/s10711-008-9281-x
For a given 0 , we show that there exist two finite index subgroups of PSL2(Z) which are (1+) -quasisymmetrically conjugated and the conjugation homeomorphism is not conformal. This implies that for any 0 there are two finite regular covers of the Modular once punctured torus T 0 (or just the Modular torus) and a (1+) -quasiconformal map between them that is not homotopic to a conformal map. As an application of the above results, we show that the orbit of the basepoint in the Teichmüller space T(S p ) of the punctured solenoid S p under the action of the corresponding Modular group (which is the mapping class group of S p , ) has the closure in T(S p ) strictly larger than the orbit and that the closure is necessarily uncountable.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||Geometriae Dedicata|
|Page Range:||pp. 145-165|
|Access rights to Published version:||Restricted or Subscription Access|
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