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Filling sets of curves on punctured surfaces

2015/08/14 by Federica Fanoni, Fanoni, Federica, Hugo Parlier +1
Computer Science · Mathematics · #30F45 (Secondary) #57M99 (Primary) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1508.03503

openalex publication_date 2015/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study filling sets of simple closed curves on punctured surfaces. In particular we study lower bounds on the cardinality of sets of curves that fill and that pairwise intersect at most k times on surfaces with given genus and number of punctures. We are able to establish orders of growth for even k and show that for odd k the orders of growth behave differently. We also study the corresponding questions when one requires that the curves be represented as systoles on hyperbolic complete finite area surfaces.

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