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Automorphisms of fine curve graphs for nonorientable surfaces
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- Journal:
- Glasgow Mathematical Journal , First View
- Published online by Cambridge University Press:
- 16 January 2025, pp. 1-13
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The fine curve graph of a surface was introduced by Bowden, Hensel, and Webb as a graph consisting of essential simple closed curves in the surface. Long, Margalit, Pham, Verberne, and Yao proved that the automorphism group of the fine curve graph of a closed orientable surface is isomorphic to the homeomorphism group of the surface. In this paper, based on their argument, we prove that the automorphism group of the fine curve graph of a closed nonorientable surface
$N$ of genus 
$g \geq 4$ is isomorphic to the homeomorphism group of 
$N$.
