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Triangulations and homology of Riemann surfaces

Authors: Peter Buser and Mika Seppälä
Journal: Proc. Amer. Math. Soc. 131 (2003), 425-432
MSC (2000): Primary 30F45; Secondary 57M20
Published electronically: September 25, 2002
MathSciNet review: 1933333
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Abstract: We derive an algorithmic way to pass from a triangulation to a homology basis of a (Riemann) surface. The procedure will work for any surfaces with finite triangulations. We will apply this construction to Riemann surfaces to show that every compact hyperbolic Riemann surface $X$ has a homology basis consisting of curves whose lengths are bounded linearly by the genus $g$ of $X$and by the homological systole.

This work got started by comments presented by Y. Imayoshi in his lecture at the 37th Taniguchi Symposium which took place in Katinkulta near Kajaani, Finland, in 1995.

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

  • 1. Lipman Bers.
    Finite dimensional Teichmüller spaces and generalizations.
    Bull. Amer. Math. Soc., 5(2):131 - 172, September 1981. MR 82k:32050
  • 2. Lipman Bers.
    An Inequality for Riemann Surfaces.
    In Isaac Chavel and Hersel M. Farkas, editors, Differential Geometry and Complex Analysis, pages 87 - 93. Springer-Verlag, Berlin-Heidelberg-New York, 1985. MR 86h:30076
  • 3. Peter Buser.
    The collar theorem and examples.
    Manuscripta Math., 25:349-357, 1978. MR 80h:53046
  • 4. Peter Buser.
    Geometry and Spectra of Compact Riemann Surfaces.
    Birkhäuser Verlag, Basel-Boston-New York, 1992. MR 93g:58149
  • 5. Peter Buser and Mika Seppälä.
    Symmetric pants decompositions of Riemann surfaces.
    Duke Math. J., 67(1):39-55, 1992. MR 93i:32026
  • 6. Peter Buser and Mika Seppälä.
    Short homology bases and partitions of Riemann surfaces.
    Topology, to appear.
  • 7. Peter Buser, Mika Seppälä and Robert Silhol.
    Triangulations and moduli spaces of Riemann surfaces with group actions.
    Manuscripta Math., 88:209-224, 1995. MR 96k:32040
  • 8. Isaac Chavel and Edgar A. Feldman.
    Cylinders on surfaces.
    Comment. Math. Helv., 53:439-447, 1978. MR 58:12830
  • 9. B. Delaunay.
    Sur la sphére vide.
    Proceedings of the International Mathematical Congress held in Toronto August 11-16, Toronto: University of Toronto Press, 695-700, 1928.
  • 10. L. Fejes Tóth.
    Kreisausfüllungen der hyperbolischen Ebene.
    Acta Math. Acad. Sci. Hungar., (4):103-110, 1953.

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Additional Information

Peter Buser
Affiliation: Département de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, CH–1007 Lausanne, Switzerland

Mika Seppälä
Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306
Address at time of publication: Department of Mathematics, University of Helsinki, FIN–00014 Helsinki, Finland
Email:, Mika.Seppala@Helsinki.Fi

Keywords: Triangulation, homology, Riemann surfaces
Received by editor(s): April 23, 2001
Received by editor(s) in revised form: July 11, 2001
Published electronically: September 25, 2002
Additional Notes: The research of the first author was supported by the Swiss National Research Foundation
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2002 American Mathematical Society