Combinatorial k-systoles on a punctured torus and a pair of pants

2021/08/18 by Diop, ElHadji Abdou Aziz, Gaye, Masseye, Sane, Abdoul Karim
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2108.08379

Abstract

In this paper, S denotes a surface homeomorphic to a punctured torus or a pair of pants. Our interest is the study of \emphcombinatorial k-systoles that is closed curves with self-intersection numbers greater than k and with least combinatorial length. We show that the maximal intersection number I^c_k of combinatorial k-systoles of S grows like k and \undersetk→+∞\limsup(I^c_k-k)=+∞. This result, in case of a pair of pants and a punctured torus, is a positive response to the combinatorial version of the Erlandsson - Parlier conjecture, originally formulated for the geometric length.

Related

• Filling sets of curves on punctured surfaces
• Self-intersection numbers of curves on the punctured torus
• Curves on the torus intersecting at most k times
• Hyperbolic punctured spheres without arithmetic systole maximizers
• Modular systoles are extremal for the crossing number