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.
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Ilya Kapovich, Paul Schupp, Delzant's -invariant, Kolmogorov complexity and one-relator groups. Comment. Math. Helv. 80 (2005), no. 4, pp. 911–933DOI 10.4171/CMH/39