Delzant's -invariant, Kolmogorov complexity and one-relator groups
Ilya Kapovich
University of Illinois at Urbana-Champaign, USAPaul Schupp
University of Illinois at Urbana-Champaign, USA
![Delzant's $T$-invariant, Kolmogorov complexity and one-relator groups cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserials%2Fcover-cmh.png&w=3840&q=90)
Abstract
We prove that for “random” one-relator groups the Delzant -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.
Cite this article
Ilya Kapovich, Paul Schupp, Delzant's -invariant, Kolmogorov complexity and one-relator groups. Comment. Math. Helv. 80 (2005), no. 4, pp. 911–933
DOI 10.4171/CMH/39