Brunnian Braids and Lie Algebras
J.Y. Li, V. V. Vershinin, J. Wu
TL;DR
This paper explores the algebraic structure of Brunnian braids, revealing their connection to homotopy groups of spheres and providing a presentation of the associated graded Lie algebra.
Contribution
It introduces a presentation of the graded Lie algebra related to the Brunnian subgroup of the pure braid group, advancing understanding of their algebraic properties.
Findings
Established a presentation of the graded Lie algebra for Brunnian braids
Linked Brunnian braids to homotopy groups of spheres
Enhanced algebraic understanding of the Brunnian subgroup
Abstract
Brunnian braids have interesting relations with homotopy groups of spheres. In this work, we study the graded Lie algebra of the descending central series related to Brunnian subgroup of the pure braid group. A presentation of this Lie algebra is obtained.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Geometric and Algebraic Topology