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Realizing pairs of
multicurves as cylinders on translation surfaces
Juliet Aygun, Janet Barkdoll, Aaron Calderon, Jenavie Lorman and Theodore Sandstrom |
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Algebraic & Geometric Topology 25 (2025) 5031–5057
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Abstract |
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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. |
Keywords
translation surfaces, cylinders, multicurves
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Mathematical Subject Classification
Primary: 57K20
Secondary: 30F30
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References |
Publication
Received: 22 April 2024
Revised: 31 July 2024
Accepted: 6 January 2025
Published: 20 November 2025
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Authors |
| Juliet Aygun | |
| Department of Mathematics Cornell University Ithaca, NY United States |
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| Janet Barkdoll | |
| Swarthmore, PA United States |
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| Aaron Calderon | |
| Department of Mathematics University of Chicago Chicago, IL United States |
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| Jenavie Lorman | |
| Prairie Village, KS United States |
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| Theodore Sandstrom | |
| Department of Mathematics,
Statistics, and Computer Science University of Illinois Chicago Chicago, IL United States |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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