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Electronic Research Announcements

ISSN 1079-6762



On non-separating simple closed curves in a compact surface

Author: Feng Luo
Journal: Electron. Res. Announc. Amer. Math. Soc. 1 (1995), 18-25
MSC (1991): Primary 57
MathSciNet review: 1336696
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Abstract: We introduce a semi-algebraic structure on the set $\mathcal {S}$ 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 group of the surface are discussed.

References [Enhancements On Off] (What's this?)

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Additional Information

Feng Luo

Keywords: Simple closed curve, surface
Received by editor(s): April 22, 1995
Received by editor(s) in revised form: March 22, 1995
Communicated by: Walter Neumann
Article copyright: © Copyright 1995 American Mathematical Society