On residual properties of pure braid groups of closed surfaces

TL;DR

This paper investigates the residual properties of pure braid groups on closed surfaces, establishing their structure as almost-direct products of residually torsion free nilpotent groups and proving residual nilpotency for 2-strand braid groups.

Contribution

It demonstrates that pure braid groups of closed surfaces are residually torsion free nilpotent and shows that 2-strand braid groups on closed surfaces are residually nilpotent.

Findings

Pure braid groups are almost-direct products of residually torsion free nilpotent groups.

Pure braid groups of closed surfaces are residually torsion free nilpotent.

Braid groups on 2 strands of closed surfaces are residually nilpotent.

Abstract

We prove that pure braid groups of closed surface are almost-direct products of residually torsion free nilpotent groups and hence residually torsion free nilpotent. As a Corollary, we prove also that braid groups on 2 strands of closed surfaces are residually nilpotent.