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arxiv: 2309.16041 · v1 · pith:HXQEFLYX · submitted 2023-09-27 · math.GT

Automorphisms of the fine 1-curve graph

Katherine Williams Booth , Daniel Minahan , Roberta Shapiro This is my paper

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classification math.GT
keywords graphcurvefinesurfaceclosedgroupverticeswhose
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The fine 1-curve graph of a surface is a graph whose vertices are simple closed curves on the surface and whose edges connect vertices that intersect in at most one point. We show that the automorphism group of the fine 1-curve graph is naturally isomorphic to the homeomorphism group of a closed, orientable surface with genus at least one.

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  1. Large flats in large subgraphs of fine curve graphs

    math.GT 2026-04 unverdicted novelty 7.0

    Fibers over vertices of the curve graph contain flats of arbitrary finite dimension, so they are not hyperbolic, and distance bounds are computed for single-isotopy-class fine curve graphs.