Realizing pairs of multicurves as cylinders on translation surfaces

Juliet Aygun; Janet Barkdoll; Aaron Calderon; Jenavie Lorman; Theodore Sandstrom

doi:10.2140/agt.2025.25.5031

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arXiv · 2404.08096

Realizing pairs of multicurves as cylinders on translation surfaces

Juliet Aygun·Janet Barkdoll·Aaron Calderon·Jenavie Lorman·Theodore Sandstrom

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Abstract

Any pair of intersecting cylinders on a translation surface is "coherent," in that the geometric and algebraic intersection numbers of their core curves are equal (up to sign). In this paper, we investigate when a pair of multicurves can be simultaneously realized as the core curves of cylinders on some translation surface. Our main tools are surface topology and the "flat grafting" deformation introduced by Ser-Wei Fu.

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Juliet Aygun, Janet Barkdoll, Aaron Calderon, Jenavie Lorman, Theodore Sandstrom. 2024-04-11. Realizing pairs of multicurves as cylinders on translation surfaces. https://doi.org/10.2140/agt.2025.25.5031

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