The Chas-Sullivan conjecture for a surface of infinite genus

Details The Chas-Sullivan conjecture for a surface of infinite genus The Chas-Sullivan conjecture for a surface of infinite genus

2010-09-25

arxiv.org/abs/1009.4985v2

Mathematics

Geometric Topology

23 pages, 13 figures. A serious error in the previous version is corrected; an appendix is added

Scientific paper

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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