Counting curve types

2016/06/20 by Aougab, Tarik, Souto, Juan · 2 citations
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1606.06067

Abstract

Let S be a closed orientable hyperbolic surface, and let O(K,S) denote the number of mapping class group orbits of curves on S with at most K self-intersections. Building on work of Sapir [16], we give upper and lower bounds for O(K,S) which are both exponential in √(K).

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• Generalizations of the Crossing Lemma
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