JournalscmhVol. 80, No. 4pp. 911–933

Delzant's TT-invariant, Kolmogorov complexity and one-relator groups

  • Ilya Kapovich

    University of Illinois at Urbana-Champaign, USA
  • Paul Schupp

    University of Illinois at Urbana-Champaign, USA
Delzant's $T$-invariant, Kolmogorov complexity and one-relator groups cover

Abstract

We prove that for ``random'' one-relator groups the Delzant TT-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 TT-invariant, Kolmogorov complexity and one-relator groups. Comment. Math. Helv. 80 (2005), no. 4, pp. 911–933

DOI 10.4171/CMH/39