Explicit Lie bracket of closed geodesics on a hyperbolic surface with applications

Moira Chas; Arpan Kabiraj

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arXiv · 2308.02006

Explicit Lie bracket of closed geodesics on a hyperbolic surface with applications

Moira Chas·Arpan Kabiraj

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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.

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Moira Chas, Arpan Kabiraj. 2023-04-21. Explicit Lie bracket of closed geodesics on a hyperbolic surface with applications. https://arxiv.org/abs/2308.02006

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