Any 3-manifold 1-dominates at most finitely many 3-manifolds of 𝑆³-geometry

DOI10.1090/S0002-9939-02-06438-9zbMath1002.57042OpenAlexW1527934022WikidataQ102428468 ScholiaQ102428468MaRDI QIDQ4536078

Claude Hayat-Legrand, Shi Cheng Wang, Heiner Zieschang

Publication date: 17 June 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-02-06438-9

zbMATH Keywords

spherical 3-manifoldsdegree 1 maps between 3-manifolds

Mathematics Subject Classification ID

Degree, winding number (55M25) General geometric structures on low-dimensional manifolds (57M50)

Related Items (5)

Heegaard genus, degree‐one maps, and amalgamation of 3‐manifolds ⋮ Volume-convergent sequences of Haken 3-manifolds. ⋮ Epimorphism sequences between hyperbolic 3-manifold groups ⋮ Nonzero degree maps between closed orientable three-manifolds ⋮ Generalized Hopfian property, a minimal Haken manifold, and epimorphisms between 3-manifold groups

Cites Work

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• Non-zero degree maps and surface bundles over \(S^ 1\)
• Non-Haken 3-manifolds are not large with respect to mappings of non-zero degree
• Maps between Seifert fibered spaces of infinite \(\pi_ 1\)
• Degree-one maps onto lens spaces
• Sequences of degree-one maps between geometric 3-manifolds
• Degree one maps of Seifert manifolds and a note on Seifert volume
• Degree One Maps Between Geometric 3-Manifolds
• The Geometries of 3-Manifolds
• Non-zero degree maps to hyperbolic \(3\)-manifolds

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