On non-separating simple closed curves in a compact surface

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Abstract

We introduce a semi-algebraic structure on the set script capital L sign of all isotopy classes of non-separating simple closed curves in any compact oriented surface and show that the structure is finitely generated. As a consequence, we produce a natural finite dimensional linear representation of the mapping class group of the surface. Applications to the Teichmüller space, Thurston's measured lamination space, the harmonic Beltrami differentials, and the first cohomology groups of the surface are discussed.

Original languageEnglish (US)
Pages (from-to)381-410
Number of pages30
JournalTopology
Volume36
Issue number2
DOIs
StatePublished - Mar 1997

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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