Curve graphs on surfaces of infinite type
Ariadna Fossas, Hugo Parlier
TL;DR
This paper introduces and analyzes analogs of curve graphs for infinite type surfaces, demonstrating their connectivity, infinite diameter, and infinite rank, based on geometric and topological properties of infinite multicurves.
Contribution
It defines new curve graph analogs for infinite type surfaces and establishes their fundamental properties, extending classical finite-type surface theory.
Findings
Graphs are generally connected
Graphs have infinite diameter
Graphs possess infinite rank
Abstract
We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense. We show that the graphs we construct are generally connected, infinite diameter and infinite rank.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Geometric and Algebraic Topology · Computational Geometry and Mesh Generation