arXiv subjects

Tam Cheetham-West

Publications and source records attributed to Tam Cheetham-West.

4 recordsLinked to original sources

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

Taut polynomials from finite quotients of fibered hyperbolic 3-manifold groups

We prove that the finite quotients of a fibered hyperbolic 3-manifold group detect the taut polynomials of fibered faces of the Thurston norm balls, whenever the monodromy map is fully-punctured. Toward this, we develop a general framework for the profinite invariance of twisted multivariable Alexander polynomials. We also identify specific hyperbolic one-cusped 3-manifolds that are profinitely rigid, by a strategy using normalized dilatations and the veering census.

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↗