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The Chas-Sullivan conjecture for a surface of infinite genus

Let Σ∞,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 Σ∞,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.