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. doi:10.1007/s10711-008-9281-x ISSN 0046-5755.

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Abstract

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 [6], [7]) 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, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Geometriae Dedicata
Publisher:	Springer
ISSN:	0046-5755
Official Date:	October 2008
Dates:	Date Event October 2008 Published
Volume:	Vol.136
Number:	No.1
Page Range:	pp. 145-165
DOI:	10.1007/s10711-008-9281-x
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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