an:05814083
Zbl 1207.20045
Rivin, Igor
Zariski density and genericity
EN
Int. Math. Res. Not. 2010, No. 19, 3649-3657 (2010).
00269276
2010
j
20G35 22E40 20H05 20E07
Zariski dense subgroups; special linear groups; symplectic groups; complex algebraic groups; generic free group automorphisms
The paper combines a number of results (some due to the author, some not) to show that Zariski density is, in a strong sense, a generic property of subgroups of \(\text{SL}(n,\mathbb{Z})\) and \(\text{Sp}(2n,\mathbb{Z})\). Theorem 4.1, stated as a joint result with Ilya Kapovich, asserts that a generic free group automorphism is hyperbolic.
The author is not careful with some statements. For example, in Remark 2.3, \(\mathbb{Z}_p\) probably means \(G(\mathbb{Z}_p\)). In Theorem 2.6, \(g_p\) should not be a scalar matrix.
L. N. Vaserstein (University Park)