Algebraic & Geometric Topology

Center of the Goldman Lie algebra

Arpan Kabiraj

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Abstract

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.

Article information

Source
Algebr. Geom. Topol., Volume 16, Number 5 (2016), 2839-2849.

Dates
Received: 19 February 2015
Revised: 13 December 2015
Accepted: 24 December 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841230

Digital Object Identifier
doi:10.2140/agt.2016.16.2839

Mathematical Reviews number (MathSciNet)
MR3572350

Zentralblatt MATH identifier
1369.57019

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 57M07: Topological methods in group theory 57M05: Fundamental group, presentations, free differential calculus

Keywords
Goldman Lie algebra hyperbolic surfaces

Citation

Kabiraj, Arpan. Center of the Goldman Lie algebra. Algebr. Geom. Topol. 16 (2016), no. 5, 2839--2849. doi:10.2140/agt.2016.16.2839. https://projecteuclid.org/euclid.agt/1510841230


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