Topology, Geometry, and Combinatorics of Fine Curve Graphs

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SHAPIRO-DISSERTATION-2024.pdf (3.16 MB)
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Shapiro, Roberta
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Etnyre, John
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https://hdl.handle.net/1853/75347
Abstract
The goal of this thesis is to explore curve graphs, which are combinatorial tools that encode topological information about surfaces. We focus on variants of the fine curve graph of a surface, which has its vertices essential simple closed curves on the surface and whose edges connect pairs of curves that are disjoint. We will prove various geometric, topological, and combinatorial results about these curve graph variants, including hyperbolicity (or lack thereof), contractibility of induced flag complexes, automorphism groups, and admissible induced subgraphs.
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2024-05-02
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