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Center of the Goldman Lie algebra

Arpan Kabiraj

Algebraic & Geometric Topology 16 (2016) 2839–2849

We show that the center of the Goldman Lie algebra associated to a closed orientable surface is generated by the class of the trivial loop. For an orientable nonclosed surface of finite type, the center is generated by closed curves which are either homotopically trivial or homotopic to boundary components or punctures.

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Goldman Lie algebra, hyperbolic surfaces
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 57M07, 57M05
Received: 19 February 2015
Revised: 13 December 2015
Accepted: 24 December 2015
Published: 7 November 2016
Arpan Kabiraj
Department of Mathematics
Indian Institute of Science
Bangalore 560012