Single self-intersection words on the once-punctured torus and their counting
arXiv:2404.09372
summary
The paper classifies closed curves on a once‑punctured torus that have exactly one self‑intersection using combinatorial methods, and then counts how many such curves exist for each word length and for different numbers of self‑intersections.
Abstract
We classify closed curves on a once-punctured torus with a single selfintersection from a combinatorial perspective. We then use the classification to determine the number of closed curves with given word-length and with zero, one, and arbitrary self-intersections.
24 pages, 7 figures
Topics & keywords
#once-punctured torus#self-intersection#closed curves#word length#enumeration#combinatorial classificationself-intersection numbercurve classificationfree group wordsmapping class groupgeodesic counting