2024/09/12 by Ian Agol, Agol, Ian, Tam Cheetham-West +3 · 1 citation
Engineering · Mathematics · #57K32 #Advanced Topics in Algebra #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Mathematics and Applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2409.08418
openalex publication_date 2024/09/12 · openalex created_date 2024/10/23 · openalex updated_date 2026/07/28
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,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.