On the asphericity of LOT-presentations of groups

Abstract

Let $U$ be an arbitrary word in letters $x_1^{\pm 1},...,x_m^{\pm 1}$ and $m\ge 2$. We prove that the group presentation $<x_1,...,x_m\Vert U{x}_i{U}^{-1}=x_{i+1},i=1,...,m-1>$ is aspherical. The proof is based upon prior partial results of A. Klyachko and the author on the asphericity of such presentations.

3 pages