On representation varie ties of some HNN-extensions of free groups

Abstract

In the article we provide the description of the structure and the properties of representation varieties Rn(G(p,q)) of the groups with the presentation G(p,q) = ‹x1,…, x2, t|t(x12…xg2)q›, where g ≥ 3, |p| > q ≥ 1. Irreducible components of Rn(G(p,q)) are found, their dimensions are calculated and it is proved, that every irreducible component of Rn(G(p,q)) is a rational variety.

Keywords

• a group presentation
• a representation variety
• a dimension of a variety
• a rational variety