2005/09/30 by Igor Belegradek · 1 citation
Computer Science · Mathematics · #3-manifold #Closed manifold #Combinatorics #Dimension (graph theory) #Fundamental group #Geometric and Algebraic Topology #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Invariant manifold #Manifold (fluid mechanics) #Mathematics #Physics #Polyhedron #Pure mathematics #Retract #Simplicial complex #Topological and Geometric Data Analysis #math.GR #math.GT #msc:20F65
paper · pdf · doi:10.2140/agt.2006.6.1341
published as Algebr. Geom. Topol. 6 (2006) 1341-1354 · This is the version published by Algebraic & Geometric Topology on 20 September 2006
openalex publication_date 2006/09/20 · arxiv created 2009/04/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract. This paper contains examples of closed aspherical manifolds obtained as a by-product of recent work by the author [Bel] on the relative strict hyperbolization of polyhedra. The following is proved. (I) Any closed aspherical triangulated n-manifold M n with hyperbolic fundamental group is a retract of a closed aspherical triangulated (n + 1)manifold N n+1 with hyperbolic fundamental group. (II) If B1,... Bm are closed aspherical triangulated n-manifolds, then there is a closed aspherical triangulated manifold N of dimension n + 1 such that N has nonzero simplicial volume, N retracts to each Bk, and π1(N) is hyperbolic relative to π1(Bk)’s. (III) Any finite aspherical simplicial complex is a retract of a closed aspherical triangulated manifold with positive simplicial volume and nonelementary relatively hyperbolic fundamental group. 1.