The \(\pi_ 1\)-injectivity of self-maps of nonzero degree on 3-manifolds

DOI10.1007/BF01459495zbMath0793.57008OpenAlexW2080126826MaRDI QIDQ1318001

Shi Cheng Wang

Publication date: 25 August 1994

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165125

zbMATH Keywords

hyperbolic 3-manifoldHaken manifoldSeifert manifoldgeometric 3- manifoldinjectivity of map induced on the fundamental groupnon- zero degree proper mapselfmap of degree larger than 1torus bundle over the circle

Mathematics Subject Classification ID

Related Items (11)

On self-mapping degrees of \(S^{3}\)-geometry manifolds ⋮ Cartesian powers of 3-manifolds ⋮ Amenable category and complexity ⋮ Self-mapping degrees of 3-manifolds ⋮ On a problem of Hopf for circle bundles over aspherical manifolds with hyperbolic fundamental groups ⋮ Local rigidity of aspherical three-manifolds ⋮ Ordering Thurston’s geometries by maps of nonzero degree ⋮ Self-mapping degrees of torus bundles and torus semi-bundles ⋮ Homomorphisms of nonzero degree betweenPD_n-groups ⋮ Finiteness of mapping degrees and \(\text{PSL}(2,R\mathbf)\)-volume on graph manifolds ⋮ On the monotonicity of amenable category

Cites Work

• Volume and bounded cohomology
• Deformation of maps to branched coverings in dimension two
• The Gromov invariant of links
• The existence of maps of nonzero degree between aspherical 3-manifolds
• Maps Inducing Isomorphisms on Fundamental Groups of Compact 3 -Manifolds
• Degree One Maps Between Geometric 3-Manifolds
• π₁ -Injective Mappings of Compact 3-Manifolds
• The Geometries of 3-Manifolds
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