Generalized Hopfian property, minimal Haken manifold, and J. Simon's conjecture for 3-manifold groups

2000/02/01 by Alan W. Reid, Reid, Alan W., Shicheng Wang +3
Mathematics · #57M #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M

paper · pdf · doi:10.48550/arxiv.math/0002003

15 pages

arxiv created 2000/02/01 · arxiv updated 2009/11/30

Abstract

We address a conjecture that π₁-surjective maps between closed aspherical 3-manifolds having the same rank on π₁ must be of non-zero degree. The conjecture is proved for Seifert manifolds, which is used in constructing the first known example of minimum Haken manifold. Another motivation is to study epimorphisms of 3-manifold groups via maps of non-zero degree between 3-manifolds.

Related

• Non-zero degree maps between 3-manifolds
• Non-zero degree maps between closed orientable three-manifolds
• Rank and genus of 3-manifolds
• Epimorphisms of 3-manifold groups
• Finiteness of 3-manifolds associated with non-zero degree mappings