2012/02/29 by Eric Chesebro, Jason DeBlois · 1 citation
Mathematics · #Algebraic number #Commensurability (mathematics) #Congruence (geometry) #Geodesic #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Pure mathematics #math.GT #msc:57M50
paper · pdf · doi:10.2140/pjm.2014.267.341
published as Pacific J. Math. 267 (2014) 341-398 · Minor changes following referee's suggestions
arxiv created 2013/09/03 · openalex publication_date 2014/05/11 · arxiv updated 2016/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We construct a family of hyperbolic link complements by gluing tangles along totally geodesic four-punctured spheres, then investigate the commensurability relation among its members. Those with different volume are incommensurable, distinguished by their scissors congruence classes. Mutation produces arbitrarily large finite subfamilies of nonisometric manifolds with the same volume and scissors congruence class. Depending on the choice of mutation, these manifolds may be commensurable or incommensurable, distinguished in the latter case by cusp parameters. All have trace field (i,