Automorphisms of smooth fine curve graphs
Katherine Williams Booth
TL;DR
This paper investigates the automorphisms of fine curve graphs on closed surfaces of genus at least 2, demonstrating they are induced by surface homeomorphisms, thus linking graph symmetries to surface symmetries.
Contribution
The paper establishes that automorphisms of the fine curve graph correspond precisely to surface homeomorphisms for closed surfaces of genus at least 2.
Findings
Automorphisms of the fine curve graph are induced by surface homeomorphisms.
The result applies to continuously k-differentiable curves on closed surfaces.
The work extends understanding of the symmetry structure of curve graphs.
Abstract
In this paper, we consider the automorphisms of fine curve graphs restricted to continuously -differentiable curves. We show that for closed surfaces with genus at least 2, they are induced by homeomorphisms of the surface.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Topological and Geometric Data Analysis · Geometric and Algebraic Topology