Abstract
For the genus 1 surface with n punctures F 1,n , we show that the Hatcher–Thurston complex \({\fancyscript{HT}(F_{1,n})}\) is hyperbolic. For the genus 2 closed surface F 2, we show that the Hatcher–Thurston complex \({\fancyscript{HT}(F_{2})}\) is strongly relatively hyperbolic with respect to a family of its subspaces {X γ }, where γ ranges over all separating curves of F 2, and each X γ is isometric to the product of two Farey graphs.
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Li, Y., Ma, J. Hyperbolicity of the genus two Hatcher–Thurston complex. Math. Z. 273, 363–378 (2013). https://doi.org/10.1007/s00209-012-1009-9
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DOI: https://doi.org/10.1007/s00209-012-1009-9