5 papers
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…
Isospectrality and isometry groups for infinite-type hyperbolic surfaces with discrete length spectrum
Federica Fanoni, David Fisac
We study infinite-type hyperbolic surfaces with discrete length spectrum. In this setup, we show that Sunada's method can only produce finite isospectral families, but that there i…
Markov's Conjecture on integral necklaces
David Fisac
We use the geometric reformulation of Markov's uniqueness conjecture in terms of the simple length spectrum on the modular torus to rewrite the conjecture in combinatorial terms by…
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…
A Basmajian-type inequality for Riemannian surfaces
Florent Balacheff, David Fisac
We explore for compact Riemannian surfaces whose boundary consists of a single closed geodesic the relationship between orthospectrum and boundary length. More precisely, we establ…