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.
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- 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
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 425-432
- MSC (2000): Primary 30F45; Secondary 57M20
- DOI: https://doi.org/10.1090/S0002-9939-02-06470-5
- MathSciNet review: 1933333