Quasipositive braids and connected sums

TL;DR

This paper establishes that the property of quasipositivity for links is preserved under connected sums, providing a characterization that links the quasipositivity of the sum to its summands using the filling disk technique.

Contribution

It proves a necessary and sufficient condition for the quasipositivity of connected sums of links, advancing understanding of link properties in knot theory.

Findings

Connected sum of quasipositive links is quasipositive.

Quasipositivity of links is characterized by their summands.

Filling disk technique is used to prove the main result.

Abstract

We prove that the connected sum of two links is quasipositive if and onlyif each summand is quasipositive. The prove is based on the filling disk technique