Small filling sets of curves on a surface

2009/09/10 by James W. Anderson, Anderson, James W., Hugo Parlier +3 · 1 citation
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.0909.1966

11 pages, 5 figures

arxiv created 2010/10/08 · arxiv updated 2010/10/11

Abstract

We show that the asymptotic growth rate for the minimal cardinality of a set of simple closed curves on a closed surface of genus g which fill and pairwise intersect at most K≥ 1 times is 2√(g)/√(K) as g → ∞ . We then bound from below the cardinality of a filling set of systoles by g/log(g). This illustrates that the topological condition that a set of curves pairwise intersect at most once is quite far from the geometric condition that such a set of curves can arise as systoles.

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