We bound the geodesic residual finiteness growths of closed hyperbolic manifolds that immerse totally geodesically in non-compact right-angled reflection orbifolds, extending work of the fourth author from the compact case. We describe a rich class of arithmetic examples to which this result applies, and apply the theorem to give effective bounds on the geodesic residual finiteness growths of m...

Let G D ha; b; : : : j r D 1i be a one-relator group equipped with at least two generators. For all w which do not commute with r in the ambient free group on the generators a, b, ..., the groups G.r;w/ D ha; b; : : : j rrw D r2i are not residually finite and have the same finite images as G. The existence of this family of one-relator groups which are not residually finite reinforces what is b...

We prove that if M is a monoid and A a finite set with more than one element, then the residual finiteness of M is equivalent to that of the monoid consisting of all cellular automata over M with alphabet A.

We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable hyperbolic group is residually finite. As a result, we are able to prove that the group of outer automorphisms of every finitely generated Fuchsian group and of every free-by-finite group is residually finite.

We prove that if every hyperbolic group is residually finite, then every quasi-convex subgroup of every hyperbolic group is separable. The main tool is relatively hyperbolic Dehn filling.