2012/08/31 by Genevieve Walsh, Genevieve S. Walsh · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Boundary (topology) #Bumping #Combinatorics #Computer science #Condensed matter physics #Conformal map #Core (optical fiber) #Discontinuity (linguistics) #Domain (mathematical analysis) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Kleinian group #Mathematical analysis #Mathematical proof #Mathematics #Physics #Pure mathematics #Set (abstract data type) #Submanifold #Topology (electrical circuits) #math.GT #msc:57M60
paper · pdf · doi:10.2140/agt.2014.14.283
published in Algebraic & Geometric Topology 14(1), 283-297 (Mathematical Sciences Publishers) · 12 pages, 2 figures; non-mathematical error fixed (The author's name is now on the title page.)
arxiv created 2012/09/18 · openalex publication_date 2014/01/09 · arxiv updated 2014/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show here that the Nielsen core of the bumping set of the domain of discontinuity of a Kleinian group is the boundary of the characteristic submanifold of the associated 3-manifold with boundary. Some examples of interesting characteristic submanifolds are given. We also give a construction of the characteristic submanifold directly from the Nielsen core of the bumping set. The proofs are from "first principles", using properties of uniform domains and the fact that quasi-conformal discs are uniform domains.