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

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.

arXiv comment24 pages, 14 figures. From the previous version, the title of the paper has been changed. Some references are updated

References in corpus (3)

• Cohomological Aspects of Magnus Expansions
• Harmonic Magnus Expansion on the Universal Family of Riemann Surfaces
• The logarithms of Dehn twists

Cited by in corpus (1)

• The Lie algebra of rooted planar trees