4 papers · 1 filter
Curves on the torus intersecting at most k times
Tarik Aougab, Jonah Gaster
We show that any set of distinct homotopy classes of simple closed curves on the torus that pairwise intersect at most times has size . Prior to this wo…
The sum of Lagrange numbers
Jonah Gaster, Brice Loustau
Combining McShane's identity on a hyperbolic punctured torus with Schmutz's work on the Markov Uniqueness Conjecture (MUC), we find that MUC is equivalent to the identity \begin{eq…
Good stackings, bislim structures, and invariant staggerings
Jacob Bamberger, David Carrier, Jonah Gaster +1
Two seemingly different properties of 2-complexes were developed concurrently as criteria for the nonpositive immersion property: 'good stackings' and 'bislim structures'. We estab…
A short proof of a conjecture of Aougab-Huang
Jonah Gaster
In response to Sanki-Vadnere, we present a short proof of the following theorem: a pair of simple curves on a hyperbolic surface whose complementary regions are disks has length at…