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
DOI:
https://doi.org/10.1090/S1079-6762-95-01003-1
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.
- Max Dehn, Papers on group theory and topology, Springer-Verlag, New York, 1987. Translated from the German and with introductions and an appendix by John Stillwell; With an appendix by Otto Schreier. MR 881797
- Travaux de Thurston sur les surfaces, Astérisque, vol. 66, Société Mathématique de France, Paris, 1979 (French). Séminaire Orsay; With an English summary. MR 568308
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- Stephen P. Humphries, Generators for the mapping class group, Topology of low-dimensional manifolds (Proc. Second Sussex Conf., Chelwood Gate, 1977) Lecture Notes in Math., vol. 722, Springer, Berlin, 1979, pp. 44–47. MR 547453
Luo, F., On non-separating simple closed curves in a compact surface, preprint.
Luo, F., On the mapping class groups of compact surfaces, in preparation.
Dehn, M., Papers on group theory and topology, J. Stillwell, ed., Springer-Verlag, New York, 1987.
Fathi, A., Laudenbach, F., Poènaru, V., Travaux de Thurston sur les surfaces, Astérisque (1979), 66-67.
Lickorish, W., A representation of oriented combinatorial 3-manifolds, Ann. Math. 72 (1962), 531-540.
Humphries, Generators for the mapping class group, Lecture Notes in Math. 722 ((1979)), Springer, Berlin, 44-47.
Luo, F., On non-separating simple closed curves in a compact surface, preprint.
Luo, F., On the mapping class groups of compact surfaces, in preparation.
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Additional Information
Feng Luo
Email:
fluo@math.rutgers.edu
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
