Explicit Lie bracket of closed geodesics on a hyperbolic surface with applications (2308.02006v1)

Abstract: In this note we develop a tool box of non-Euclidean plane geometry methods that yield a constructive way to define in terms of closed geodesics the Goldman bracket on deformation classes of closed, directed curves. We use this construction to algebraically characterize closed geodesics without self-intersection on hyperbolic surfaces.