Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2503.04116 |
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Sommario:
- Let $S_g$ be a closed orientable surface of genus $g\geq 2$. A collection $Ω= \{ γ_1, \dots, γ_s\}$ of pairwise non-homotopic simple closed curves on $S_g$ such that $γ_i$ and $γ_j$ are in minimal position, is called a \emph{filling system} or a \emph{filling} of $S_g$ if the complement $S_g\setminus Ω$ is a disjoint union of $b$ topological discs for some $b\geq 1$. The \emph{size} of a filling system is defined as the number of its elements. We prove that the maximum size of a filling system on $S_g$ with $ 1 \leq b \leq 2g-2$ boundary components is $2g+b-1$. Furthermore, we give a lower bound on mapping class group orbits of filling systems of maximum size with $ 1 \leq b \leq g-2$ boundary components.