Year: 2026
Type: preprint
Abstract: We study two fundamental properties of the intersection pairing between geodesic currents on infinite-type surfaces which are classical in the finite-type closed setting: injectivity of the marked length spectrum and continuity of the intersection form. We show that geodesic currents on infinite-type surfaces of the first kind are determined by their intersection numbers with closed curves, extending Otal's marked length spectrum rigidity argument from finite-type to infinite-type surfaces. In contrast, we prove that the intersection pairing is not continuous in general for the natural topologies by constructing explicit counterexamples. We then prove sufficient criteria for continuity of intersection numbers for infinite-type surfaces.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223337181