TL;DR
This paper characterizes the center of the Goldman algebra for hyperbolic surfaces, showing it is trivial for closed surfaces and generated by boundary-homotopic curves for surfaces with boundary.
Contribution
It provides a complete description of the center of the Goldman algebra for different types of hyperbolic surfaces, extending previous understanding.
Findings
Center is trivial for closed hyperbolic surfaces.
Center consists of boundary-homotopic curves for surfaces with boundary.
Clarifies algebraic structure related to surface topology.
Abstract
We show that the center of the Goldman algebra associated to a closed oriented hyperbolic surface is trivial. For a hyperbolic surface of finite type with nonempty boundary, the center consists of closed curves which are homotopic to boundary components or punctures.
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