Realizing pairs of multicurves as cylinders on translation surfaces
Geometric Topology
2025-11-26 v1
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.
Keywords
Cite
@article{arxiv.2404.08096,
title = {Realizing pairs of multicurves as cylinders on translation surfaces},
author = {Juliet Aygun and Janet Barkdoll and Aaron Calderon and Jenavie Lorman and Theodore Sandstrom},
journal= {arXiv preprint arXiv:2404.08096},
year = {2025}
}
Comments
19 pages, 9 figures. Comments welcome!