The universal cover of 3-manifolds built from injective handlebodies is \mathbb R³

2006/01/30 by James Coffey, Coffey, James
Mathematics · #57M #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #math.GT #msc:57M

paper · pdf · doi:10.48550/arxiv.math/0601721

21 pages, 9 figures. Minor gramatical changes

openalex publication_date 2006/01/30 · arxiv created 2007/01/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper gives a proof that the universal cover of a closed 3-manifold built from three π₁-injective handlebodies is homeomorphic to \mathbb R³. This construction is an extension to handlebodies of the conditions for gluing of three solid tori to produce non-Haken Seifert fibered manifolds with infinite fundamental group. This class of manifolds has been shown to contain non-Haken non-Seifert fibered manifolds.

Citations

• The word problem for 3-manifolds built from injective handlebodies
• The Geometries of 3-Manifolds

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