English

Word-length curve counting on the once-punctured torus

Geometric Topology 2025-11-11 v3 Combinatorics

Abstract

We classify closed curves on a once-punctured torus with a single self-intersection from a combinatorial perspective. We determine the number of closed curves with given word-length and with zero, one, and arbitrary self-intersections.

Keywords

Cite

@article{arxiv.2404.09372,
  title  = {Word-length curve counting on the once-punctured torus},
  author = {David Fisac and Mingkun Liu},
  journal= {arXiv preprint arXiv:2404.09372},
  year   = {2025}
}

Comments

24 pages, 7 figures