Simple curves on surfaces
Abstract
We show that the number of simple closed geodesics of length bounded by L on a hyperbolic surface of genus g with c cusps and b boundary components grows roughly like L6g+2b+2c-6. This has been conjectured for some time.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.