Exact curve counting of given word length on the once-punctured torus

@misc{baroni2026exact,
  title = {{Exact curve counting of given word length on the once-punctured torus}},
  author = {Filippo Baroni and David Fisac and Mingkun Liu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01382},
  eprint = {2609.01382},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01382},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Exact curve counting of given word length on the once-punctured torus
AU  - Filippo Baroni
AU  - David Fisac
AU  - Mingkun Liu
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.01382
UR  - https://arxiv.org/abs/2609.01382
AB  - On the once-punctured torus, we give an exact formula for the number of curves in any given mapping class group orbit of given word length. This settles a conjecture of Chas in [Cha16].
ER  -