Triangulations and homology of Riemann Surfaces

Peter Buser, Mika Seppälä

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 to show that every compact hyperbolic Riemann Surface X has a homology basis consisting of curves whose lenghts are bounded linearly by the genus g of X and by the homological systole.

This work got started by comments presented by Y. Imayoshi (see [9]) in his lecture at the 37th Taniguchi Symposium which took place in Katinkulta near Kajaani, Finland, in 1995.