Commentarii Mathematici Helvetici


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Volume 80, Issue 4, 2005, pp. 911–933
DOI: 10.4171/CMH/39

Published online: 2005-12-31

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

Ilya Kapovich[1] and Paul Schupp[2]

(1) University of Illinois at Urbana-Champaign, USA
(2) University of Illinois at Urbana-Champaign, USA

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

Kapovich Ilya, Schupp Paul: Delzant's $T$-invariant, Kolmogorov complexity and one-relator groups. Comment. Math. Helv. 80 (2005), 911-933. doi: 10.4171/CMH/39