Filling surfaces with very few systoles

Olivier Mathieu

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arXiv · 2606.28954

Filling surfaces with very few systoles

Olivier Mathieu

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Abstract

In the paper we describe hyperbolic surfaces filled by their systoles, where the total number of systoles is in $O(\frac{g}{\ln \,g})$, that is equivalent to the lower bound of Anderson, Parlier and Pittet \cite{APP}. Various papers \cite{SS}\cite{FB20}\cite{Sanki}\cite{ IM}\cite{ Mathieu} have investigated the same question, and the best previously known upper bounds where in $o(\frac{g}{{\sqrt{\ln \,g}}})$. Surprizingly the present approach is, in our opinion, much simpler than the methods of earlier papers.

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BibTeX RIS

Olivier Mathieu. 2026-06-27. Filling surfaces with very few systoles. https://arxiv.org/abs/2606.28954

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