Tree groups and the 4-string pure braid group
It is shown that the (unperturbed) braid group on four strings \(B_ 4\) is an HNN-extension of the graph group \(F_ 5\) of a certain graph S having 5 vertices and 5 edges. As a consequence, a conjecture due to J. Tits, referring to the structure of a suitable subgroup of the braid group, is resolved for the special case \(B_ 4\). Various other results are obtained dealing for example with the question of the linearity of the braid groups.
scientific article; zbMATH DE number 4200472