A VECTOR FIELD APPROACH TO MAPPING CLASS ACTIONS

Autor:	Nikola Lakic, Frederick P. Gardiner
Rok vydání:	2006
Předmět:	Teichmüller space Group (mathematics) General Mathematics Riemann surface Homotopy Mathematical analysis Type (model theory) Mapping class group Combinatorics Cantor set symbols.namesake Bounded function symbols Mathematics
Zdroj:	Proceedings of the London Mathematical Society. 92:403-427
ISSN:	1460-244X 0024-6115
DOI:	10.1112/s0024611505015558
Popis:	We present a vector field method for showing that certain subgroups of the mapping class group $\Gamma$ of a Riemann surface of infinite topological type act properly discontinuously. We apply the method to the group of homotopy classes of quasiconformal self-maps of the complement $\Omega$ of a Cantor set in $\mathbb{C}$. When the Cantor set has bounded geometric type, we show that $\Gamma(\Omega)$ acts on the Teichmüller space $T(\Omega)$ properly discontinuously. Also, we apply the same method to show that the pure mapping class group $\Gamma_0(\Omega \cup \{\infty\})$ acts properly discontinuously on $T(\Omega \cup \{\infty\})$.
Databáze:	OpenAIRE
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