The coarse geometry of hexagon decomposition graphs
Funda G\"ultepe, Hugo Parlier
TL;DR
This paper explores the geometric properties of graphs derived from hexagon decompositions of surfaces, revealing their quasi-isometric relationships to the pants graph and the mapping class group.
Contribution
It introduces new graphs based on hexagon decompositions and establishes their quasi-isometric equivalences to well-studied surface and group structures.
Findings
One graph is quasi-isometric to the pants graph.
Another graph is quasi-isometric to a Cayley graph of the mapping class group.
Provides new insights into the geometric structure of surface decompositions.
Abstract
We define and study graphs associated to hexagon decompositions of surfaces by curves and arcs. One of the variants is shown to be quasi-isometric to the pants graph, whereas the other variant is quasi-isometric to (a Cayley graph of) the mapping class group.
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Taxonomy
TopicsGeometric and Algebraic Topology · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory