The center of the Goldman Lie algebra of a surface of infinite genus

Nariya Kawazumi; Yusuke Kuno

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arXiv · 1009.4985

The center of the Goldman Lie algebra of a surface of infinite genus

Nariya Kawazumi·Yusuke Kuno

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Abstract

Let $\Sigma_{\infty, 1}$ be the inductive limit of compact oriented surfaces with one boundary component. We prove the center of the Goldman Lie algebra of the surface $\Sigma_{\infty,1}$ is spanned by the constant loop. A similar statement for a closed oriented surface was conjectured by Chas and Sullivan, and proved by Etingof. Our result is deduced from a computation of the center of the Lie algebra of oriented chord diagrams.

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Nariya Kawazumi, Yusuke Kuno. 2010-09-25. The center of the Goldman Lie algebra of a surface of infinite genus. https://arxiv.org/abs/1009.4985

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