English

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!