3 papers
math.GT2026
Exact curve counting of given word length on the once-punctured torus
Filippo Baroni, David Fisac, Mingkun Liu
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 [Ch…
math.GT2024
Single self-intersection words on the once-punctured torus and their counting
David Fisac, Mingkun Liu
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 close…
math.GT2023
Low-lying geodesics on the modular surface and necklaces
Ara Basmajian, Mingkun Liu
The m-thick part of the modular surface X is the smallest compact subsurface of X with horocycle boundary containing all the closed geodesics which wind around the cusp at most m t…