Delzant's T-invariant, Kolmogorov complexity and one-relator groups
| dc.creator | Kapovich, Ilya | |
| dc.creator | Schupp, Paul | |
| dc.date | 2003-05-25 | |
| dc.date | 2005-01-30 | |
| dc.date.accessioned | 2026-07-07T04:58:16Z | |
| dc.date.available | 2026-07-07T04:58:16Z | |
| dc.description | We prove that ``almost generically'' for a one-relator group Delzant's $T$-invariant (which measures the smallest size of a finite presentation for 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. We also give a precise asymptotic estimate (when $k$ is fixed and $n$ goes to infinity) for the number $I_{k,n}$ of isomorphism classes of $k$-generator one-relator groups with a cyclically reduced defining relator of length $n$: \[ I_{k,n}\sim \frac{(2k-1)^n}{nk!2^{k+1}}. \] Here $f(n)\sim g(n)$ means that $\lim_{n\to\infty} f(n)/g(n)=1$. | |
| dc.description | A revised version, to appear in Comment. Math. Helv | |
| dc.identifier | https://arxiv.org/abs/math/0305353 | |
| dc.identifier | http://arxiv.org/abs/math/0305353 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67566 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | Primary 20F36, Secondary 20E36, 68Q30, 03D | |
| dc.title | Delzant's T-invariant, Kolmogorov complexity and one-relator groups | |
| dc.type | text |