|
Triangulations and homology of Riemann surfaces
Author(s):
Peter
Buser;
Mika
Seppälä
Journal:
Proc. Amer. Math. Soc.
131
(2003),
425-432.
MSC (2000):
Primary 30F45;
Secondary 57M20
Posted:
September 25, 2002
Retrieve article in:
PDF
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.
References:
-
- 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.
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
30F45,
57M20
Retrieve articles in all Journals with MSC
(2000):
30F45,
57M20
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:
10.1090/S0002-9939-02-06470-5
PII:
S 0002-9939(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
Posted:
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 of article:
Copyright
2002,
American Mathematical Society
|
Comments: webmaster@ams.org