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Involutions of spherical 3-manifolds

Mattia Mecchia, Baptiste Schilling

Abstract

We classify involutions acting on spherical 3-manifolds up to conjugacy. Our geometric approach provides insights into numerous topological properties of these involutions.

Involutions of spherical 3-manifolds

Abstract

We classify involutions acting on spherical 3-manifolds up to conjugacy. Our geometric approach provides insights into numerous topological properties of these involutions.
Paper Structure (10 sections, 4 theorems, 16 equations, 1 figure, 10 tables)

This paper contains 10 sections, 4 theorems, 16 equations, 1 figure, 10 tables.

Table of Contents

  1. Introduction
  2. Finite subgroup of SO(4)
  3. Isometry groups
  4. Involutions of spherical manifolds
  5. Geometric properties of involutions
  6. Extension given by involutions.
  7. Seifert fibrations of the quotient orbifolds.
  8. Hyperelliptic involutions.
  9. Involutions acting freely.
  10. More topological properties of the quotient orbifolds

Key Result

Theorem 1.1

Let $M$ be a spherical 3-manifold. Moreover, $M$ admits, up to conjugacy, exactly one hyperelliptic involution.

Figures (1)

  • Figure 1: Montesinos links

Theorems & Definitions (6)

  • Theorem 1.1
  • Theorem 1.2
  • Lemma 2.1
  • Lemma 3.1
  • Remark 1
  • Remark 2