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