arXiv subjects

Tam Cheetham-West

Publications and source records attributed to Tam Cheetham-West.

4 recordsLinked to original sources

arXiv2026

Finiteness of closed arithmetic hyperbolic surface bundles

For each $g\ge 2$, we show that there are finitely many cyclic commensurability classes of closed, fibered arithmetic hyperbolic $3$-manifolds with genus $g$ fiber. More generally, we show that there are only finitely many conjugacy classes of admissible surface subgroups of PSL$_2(\mathbb{C})$ whose image is contained in the fundamental group of some arithmetic hyperbolic $3$-manifold. We also give an effectively computable upper bound with effective asymptotic rate on both finiteness statements. This affirms a conjecture of Bowditch, Maclachlan, and Reid.

math.GT↗

arXiv2026

Normalizers of lattices and isometry groups of arithmetic hyperbolic manifolds

We prove that every arithmetic lattice in PSL$(2,\mathbb{C})$ and every arithmetic lattice of the simplest type in PO$(n,1)$, $n\ge 2$, is the normalizer of arbitrarily many of its sublattices. Combined with previous work, this result implies that every lattice in PSL$(2,\mathbb{C})$ has this property. In this way, we prove that the set of profinitely flexible lattices in PSL$(2,\mathbb{C})$ is either empty or countably infinite. Another result is that every finite group is realized as the full isometry group of an arithmetic hyperbolic $n$-manifold. The proof of this theorem is based on study of normalizers of lattices and subgroup growth theory.

math.GT↗

arXiv2026

Detecting embedded surfaces using finite quotients

We give conditions on a Haken hyperbolic rational homology three sphere that imply that any other 3-manifold with profinitely equivalent fundamental group must also be Haken. In the appendix, we show that a regular finite-sheeted cover of an aspherical integral homology three-sphere with positive first Betti number must have first Betti number at least four. We also show that this lower bound is sharp.

math.GT↗

arXiv2024

Simply transitive geodesics and omnipotence of lattices in PSL$(2,\mathbb{C})$

We show that the isometry group of a finite-volume hyperbolic 3-manifold acts simply transitively on many of its closed geodesics. Combining this observation with the Virtual Special Theorems of the first author and Wise, we show that every non-arithmetic lattice in PSL$(2,\mathbb{C})$ is the full group of orientation-preserving isometries for some other lattice and that the orientation-preserving isometry group of a finite-volume hyperbolic 3-manifold acts non-trivially on the homology of some finite-sheeted cover.

math.GT↗