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math.GT2026
The intersection dual of geodesic currents
DÃdac MartÃnez-Granado, Dylan P. Thurston
Geodesic currents on closed hyperbolic surfaces are measures on the unit tangent bundle invariant under geodesic flow and orientation reversal. Every geodesic current induces a dua…
math.GT2024
From curves to currents
DÃdac MartÃnez-Granado, Dylan P. Thurston
Many natural real-valued functions of closed curves are known to extend continuously to the larger space of geodesic currents. For instance, the extension of length with respect to…
math.GT2024
A bordered HF- algebra for the torus
Robert Lipshitz, Peter Ozsváth, Dylan Thurston
We describe a weighted -algebra associated to the torus. We give a combinatorial construction of this algebra, and an abstract characterization. The abstract characteriza…