Brunnian Braids on Surfaces

TL;DR

This paper identifies generators for Brunnian braids on various surfaces, expanding understanding of their algebraic structure, especially on surfaces other than the sphere or projective plane.

Contribution

It provides a comprehensive set of generators for Brunnian braids on general surfaces, including special cases like the sphere and projective plane, linking to homotopy groups.

Findings

Generators for Brunnian braids on surfaces other than S^2 and RP^2.

Generators for Brunnian braids on S^2 and RP^2 include homotopy groups of a 2-sphere.

Enhanced understanding of the algebraic structure of Brunnian braids on surfaces.

Abstract

We determine a set of generators for the Brunnian braids on a general surface $M$ for $M\not=S^2$ or $\RP^2$. For the case $M=S^2$ or $\RP^2$, a set of generators for the Brunnian braids on $M$ is given by our generating set together with the homotopy groups of a 2-sphere.