Commentarii Mathematici Helvetici
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Volume 80, Issue 4, 2005, pp. 911–933
DOI: 10.4171/CMH/39
Delzant's $T$-invariant, Kolmogorov complexity and one-relator groups
Ilya Kapovich (1) and Paul Schupp (2)
(1) Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W Green Street, IL 61801-2975, URBANA, UNITED STATES(2) Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W Green Street, IL 61801-2975, URBANA, UNITED STATES
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.
Keywords: Delzant's $T$-invariant, Kolmogorov complexity, generic groups