Extending homeomorphisms of the circle to quasiconformal homeomorphisms of the disk (Q873948)

Let \(QC\) be the group of quasiconformal homeomorphisms of the closed unit disk and let \(QS\) the group of quasisymmetric homeomorphisms of the circle. Restriction to the boundary circle gives a surjective homomorphism \(q: QC \to QS\). In this paper under review, the authors prove that there is no homomorphism \(E: QS \to QC\) such that the composite \(q \circ E\) is the identity. A detailed background on this result and an outline of the proof are given for readers.