Distance 4 curves in the curve graph of closed surfaces
APA
(2024). Distance 4 curves in the curve graph of closed surfaces. SciVideos. https://youtube.com/live/asxF501THKQ
MLA
Distance 4 curves in the curve graph of closed surfaces. SciVideos, Aug. 07, 2024, https://youtube.com/live/asxF501THKQ
BibTex
@misc{ scivideos_ICTS:29136,
doi = {},
url = {https://youtube.com/live/asxF501THKQ},
author = {},
keywords = {},
language = {en},
title = {Distance 4 curves in the curve graph of closed surfaces},
publisher = {},
year = {2024},
month = {aug},
note = {ICTS:29136 see, \url{https://scivideos.org/icts-tifr/29136}}
}
Abstract
Let Sg be a closed surface of genus g ≥ 2. The curve graph corresponding to Sg, denoted by C(Sg), is a 1-dimensional simplicial complex whose vertices are isotopy classes of essential closed curves on Sg and two vertices share an edge if they represent mutually disjoint curves. Little is known about curves which are at a distance n ≥ 4 apart in C(Sg). This is primarily because the local infinitude of the vertices in C(Sg) hinders the calculation of distances in C(Sg).
In this talk, we will look at a family of pairs of curves on Sg which are at a distance 4 apart in C(Sg). These curves are created using Dehn twists. As an application, we will deduce an upper bound on the minimal intersection number of curves at a distance 4 apart in C(Sg). Finally, we will look at an example of a pair of curves on S2 which are at a distance 5 apart in C(S2).