2 results
A hyperbolic free-by-cyclic group determined by its finite quotients
- Part of
-
- Journal:
- Glasgow Mathematical Journal , First View
- Published online by Cambridge University Press:
- 04 April 2025, pp. 1-3
-
- Article
- Export citation
-
We show that the group
$ \langle a,b,c,t \,:\, a^t=b,b^t=c,c^t=ca^{-1} \rangle$ is profinitely rigid amongst free-by-cyclic groups, providing the first example of a hyperbolic free-by-cyclic group with this property.
Profinite invariants of arithmetic groups
- Part of
-
- Journal:
- Forum of Mathematics, Sigma / Volume 8 / 2020
- Published online by Cambridge University Press:
- 13 November 2020, e54
-
- Article
-
- You have access
- Open access
- Export citation
-
We prove that the sign of the Euler characteristic of arithmetic groups with the congruence subgroup property is determined by the profinite completion. In contrast, we construct examples showing that this is not true for the Euler characteristic itself and that the sign of the Euler characteristic is not profinite among general residually finite groups of type F. Our methods imply similar results for
$\ell^2$
-torsion as well as a strong profiniteness statement for Novikov–Shubin invariants.
