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Short loop decompositions of surfaces and the geometry of jacobians

Balacheff, Florent ; Parlier, Hugo ; Sabourau, Stéphane

In: Geometric and functional analysis, 2012, vol. 22, no. 1, p. 37-73

Given a Riemannian surface, we consider a naturally embedded graph which captures part of the topology and geometry of the surface. By studying this graph, we obtain results in three different directions.First, we find bounds on the lengths of homologically independent curves on closed Riemannian surfaces. As a consequence, we show that for any l Î (0, 1) there exists a constant C λ such that...