An exact sequence for generalized string links over surfaces

TL;DR

This paper extends Goldberg's result to generalized string links over closed, orientable surfaces of genus at least one, providing an exact sequence that characterizes their algebraic structure.

Contribution

It introduces an exact sequence for generalized string links over higher-genus surfaces, expanding Goldberg's previous work beyond the sphere case.

Findings

Established an exact sequence for generalized string links over surfaces of genus g ≥ 1.

Extended Goldberg's result from the sphere to higher-genus surfaces.

Provides algebraic tools for studying string links on complex surfaces.

Abstract

In this work we extend Goldberg result \cite{Goldberg} for generalized string links over closed, connected and orientable surfaces of genus $g \geq 1$, i.e., different from the sphere (up to link-homotopy).