Delzant's $T$-invariant, Kolmogorov complexity and one-relator groups

Abstract

We prove that for “random” one-relator groups the Delzant $T$-invariant (which measures the smallest size of a finite presentation of a group) is comparable in magnitude with the length of the defining relator. The proof relies on our previous results regarding isomorphism rigidity of generic one-relator groups and on the methods of the theory of Kolmogorov–Chaitin complexity.