Matthew Zevenbergen

activity

20242026

collaborators

4 papers

math.GT2026

Arithmetic hyperbolic manifolds with bounded rank

Matthew Zevenbergen

We prove that closed arithmetic hyperbolic $n$ -manifolds of bounded rank have bounded adjoint trace field degree, and consequently have lower bounded injectivity radius. From this,…

math.GT2026

Combinations and chromatography of paths of Kleinian groups

Matthew Zevenbergen

We study continuous paths in the Chabauty topology on the set $D_{n}$ of torsion free discrete subgroups of the isometry group of $n$ -dimensional hyperbolic space. We prove…

math.GT2025

Systolic lattice extensions of classical Schottky groups

Junzhi Huang, Matthew Zevenbergen

We produce lattice extensions of a dense family of classical Schottky subgroups of the isometry group of $d$ -dimensional hyperbolic space. The extensions produced are said to be sy…

math.GT2024

Connectivity in the space of framed hyperbolic 3-manifolds

Matthew Zevenbergen

We prove that the space $H_{\infty}$ of framed infinite volume hyperbolic $3$ -manifolds is connected but not path connected. Two proofs of connectivity of this space, which…