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

Ilya Kapovich, Paul Schupp

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)911-933
Number of pages23
JournalCommentarii Mathematici Helvetici
Volume80
Issue number4
DOIs
StatePublished - 2005

Keywords

  • Delzant's T-invariant
  • Generic groups
  • Kolmogorov complexity

ASJC Scopus subject areas

  • Mathematics(all)

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