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 | References | Similar Articles | Additional Information

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 has a homology basis consisting of curves whose lengths are bounded linearly by the genus of 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.

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Short homology bases and partitions of Riemann surfaces.*Topology*, to appear.**7.**P. Buser, M. Seppälä, and R. Silhol,*Triangulations and moduli spaces of Riemann surfaces with group actions*, Manuscripta Math.**88**(1995), no. 2, 209–224. MR**1354107**, 10.1007/BF02567818**8.**Isaac Chavel and Edgar A. Feldman,*Cylinders on surfaces*, Comment. Math. Helv.**53**(1978), no. 3, 439–447. MR**0493868****9.**B. Delaunay.

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Additional Information

**Peter Buser**

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

Email:
Peter.Buser@epfl.ch

**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@fsu.edu, Mika.Seppala@Helsinki.Fi

DOI:
https://doi.org/10.1090/S0002-9939-02-06470-5

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