Open AccessTeichmüller space of a countable set of points on the Riemann sphere
Author(s) -
Masahiko Taniguchi
Publication year - 2017
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1701045t
Subject(s) - mathematics , countable set , riemann sphere , pure mathematics , holomorphic function , limit set , space (punctuation) , riemann surface , teichmüller space , set (abstract data type) , mathematical analysis , discrete mathematics , limit (mathematics) , linguistics , philosophy , computer science , programming language
We introduce the Teichm?ller space T(E) of an ordered countable set E of infinite number of distinct points on the Riemann sphere. We discuss the relation between the Teichm?ller distance on T(E) and a natural one on the configuration space for E. Also we give a system of global holomorphic coordinates for T(E) when E is determined from a finitely generated semigroup consisting of M?bius transformations with the totally disconnected forward limit set.