Hyperbolic surfaces with long systoles that form a pants decomposition

TL;DR

This paper constructs sequences of closed hyperbolic surfaces with long systoles forming pants decompositions, where the systole length grows logarithmically with the genus, advancing understanding of geometric structures.

Contribution

It introduces a novel construction of hyperbolic surfaces with long systoles that form pants decompositions, with systole length increasing logarithmically with genus.

Findings

Systole lengths grow logarithmically with genus.

Constructed surfaces have pants decompositions with long systoles.

Provides explicit sequences of hyperbolic surfaces with these properties.

Abstract

We present a construction of sequences of closed hyperbolic surfaces that have long systoles which form pants decompositions of these surfaces. The length of the systoles of these surfaces grows logarithmically as a function of their genus.