Finiteness of nonzero degree maps between three-manifolds

Abstract

In this paper, it is shown that every orientable closed 3-manifold maps with nonzero degree onto at most finitely many homeomorphically distinct irreducible non-geometric orientable closed 3-manifolds. Moreover, given any nonzero integer, as a mapping degree up to sign, every orientable closed 3-manifold maps with that degree onto only finitely many homeomorphically distinct orientable closed 3-manifolds.

34 pages, 3 figures; accepted for publication by Journal of Topology

References in corpus (3)

• Geometry, Heegaard splittings and rank of the fundamental group of hyperbolic 3-manifolds
• Roots of torsion polynomials and dominations
• Presentation length and Simon's conjecture

Cited by in corpus (5)

• Brouwer degree, domination of manifolds, and groups presentable by products
• Extending periodic automorphisms of surfaces to 3-manifolds
• 1-domination of knots
• Odd manifolds of small integral simplicial volume
• Degree one maps on four manifolds with cyclic fundamental groups