On the Lie algebras associated with pure mapping class groups

TL;DR

This paper studies the graded Lie algebra associated with the pure mapping class group of a punctured sphere, providing a simple presentation and exploring its algebraic structure.

Contribution

It offers a new simple presentation of the graded Lie algebra related to pure mapping class groups of a sphere, advancing understanding of their algebraic properties.

Findings

Derived a simple presentation of the Lie algebra

Analyzed the structure of the graded Lie algebra

Connected properties of pure braid groups and mapping class groups

Abstract

Pure braid groups and pure mapping class groups of a punctured sphere have many features in common. In the paper the graded Lie algebra of the descending central series of the pure mapping class of a sphere is studied. A simple presentation of this Lie algebra is obtained.