A four-term exact sequence of surface orbifold pure braid groups

TL;DR

This paper establishes a four-term exact sequence for surface orbifold pure braid groups in all genus ≥ 1 orientable orbifolds with cone points, correcting previous inaccuracies.

Contribution

It provides a corrected and generalized exact sequence for pure braid groups on surface orbifolds, extending prior work and addressing earlier errors.

Findings

Established a four-term exact sequence for pure braid groups on orbifolds

Corrected previous inaccuracies in the earlier published sequence

Applicable to all genus ≥ 1 orientable orbifolds with cone points

Abstract

We prove a four-term exact sequence of surface orbifold pure braid groups for all genus $\geq 1$, $2$-dimensional orientable orbifolds with cone points. This corrects our earlier result in arXiv.2106.08110.