A construction of minimal coherent filling pairs
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911612124790784 |
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| author | Chang, Hong Menasco, William W. |
| author_facet | Chang, Hong Menasco, William W. |
| contents | Let $S_g$ denote the genus $g$ closed orientable surface. A \emph{coherent filling pair} of simple closed curves, $(α,β)$ in $S_g$, is a filling pair that has its geometric intersection number equal to the absolute value of its algebraic intersection number. A \emph{minimally intersecting} filling pair, $(α,β)$ in $S_g$, is one whose intersection number is the minimal among all filling pairs of $S_g$. In this paper, we give a simple geometric procedure for constructing minimal intersecting coherent filling pairs on $S_g, \ g \geq 3,$ from the starting point of a coherent filling pair of curves on a torus. Coherent filling pairs have a natural correspondence to square-tiled surfaces, or {\em origamis}, and we discuss the origami obtained from the construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_03632 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A construction of minimal coherent filling pairs Chang, Hong Menasco, William W. Geometric Topology 2020: 57K20, 57M07, 57M15 Let $S_g$ denote the genus $g$ closed orientable surface. A \emph{coherent filling pair} of simple closed curves, $(α,β)$ in $S_g$, is a filling pair that has its geometric intersection number equal to the absolute value of its algebraic intersection number. A \emph{minimally intersecting} filling pair, $(α,β)$ in $S_g$, is one whose intersection number is the minimal among all filling pairs of $S_g$. In this paper, we give a simple geometric procedure for constructing minimal intersecting coherent filling pairs on $S_g, \ g \geq 3,$ from the starting point of a coherent filling pair of curves on a torus. Coherent filling pairs have a natural correspondence to square-tiled surfaces, or {\em origamis}, and we discuss the origami obtained from the construction. |
| title | A construction of minimal coherent filling pairs |
| topic | Geometric Topology 2020: 57K20, 57M07, 57M15 |
| url | https://arxiv.org/abs/2302.03632 |