Isometries of elliptic 3-manifolds

2000/10/08 by Darryl McCullough, McCullough, Darryl
Mathematics · #57M50 #57M60 #58D99 #Advanced Combinatorial Mathematics #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.DG #math.GT #msc:57M50 #msc:57M60 #msc:58D99

paper · pdf · doi:10.48550/arxiv.math/0010077

arxiv created 2000/10/08 · openalex publication_date 2000/10/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The closed 3-manifolds of constant positive curvature were classified long ago by Seifert and Threlfall. Using well-known information about the orthogonal group O(4), we calculate their full isometry groups Isom(M), determine which elliptic 3-manifolds admit Seifert fiberings that are invariant under all isometries, and verify that the inclusion of Isom(M) to Diff(M) is a bijection on path components.

Citations

• The Generalized Smale Conjecture for 3-manifolds with genus 2 one-sided Heegaard splittings
• The Geometries of 3-Manifolds

Related

• Diffeomorphisms of Elliptic 3-Manifolds
• Geometric structures and the Laplace spectrum, part II
• Isospectral flat 3-manifolds
• Maps from 3-manifolds to 4-manifolds that induce isomorphisms on π₁
• Finite isometry groups of 4-manifolds with positive sectional curvature