A distance on conjugacy classes of HNN decompositions of a group (Q1327729)

In the paper, the different ways are considered in which a group may be expressed as an HNN-extension with the same stable letter \(t\) (up to conjugation by powers of \(t\)). Continuing work in a previous paper, a non-negative integer-valued distance function is defined on equivalence classes of such HNN-presentations of a given group, under a suitable hypothesis, which is then calculated in some examples. The construction is motivated by HNN-decompositions of a knot group coming from incompressible spanning surfaces for a knot in the 3-sphere.