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Explicit Lie bracket of closed geodesics on a hyperbolic surface with applications (2308.02006v1)
Published 21 Apr 2023 in math.GT
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.