Myers, Robert2025-01-152025-01-151983-07Myers, R. (1983). Homology cobordisms, link concordances, and hyperbolic 3-manifolds. Transactions of the American Mathematical Society, 278(1), pp. 271-288. https://doi.org/10.1090/S0002-9947-1983-0697074-40002-9947https://hdl.handle.net/20.500.14446/345769Let M³₀ and M³₁ be compact, oriented 3-manifolds. They are homology cobordant (respectively relative homology cobordant) if ∂M³ᵢ = ø (resp. ∂M³ᵢ ≠ ø) and there is a smooth, compact oriented 4-manifold W⁴ such that ∂W⁴ = M³₀ - M³₁ (resp. ∂W⁴ = M³₀ - M³₁) U (M³₁;Z) → H*(W⁴;Z) are isomorphisms, I= 0,1. Theorem. Every closed, oriented 3-manifold is homology cobordant to a hyperbolic 3-manifold. Theorem. Every compact, oriented 3-manifold whose boundary is nonempty and contains no 2-spheres is relative homology cobordant to a hyperbolic 3-manifold. Two oriented links L₀ and L₁ in a 3-manifold M³ are concordant if there is a set A² of smooth, disjoint, oriented annuli in M X [0,1] such that ∂A² = L₀ - L₁, where Lᵢ ⊆ M³ X {i}, i = 0, 1. Theorem. Every link in a compact, oriented 3-manifold M³ whose boundary contains no 2-spheres is concordant to a link whose exterior is hyperbolic. Corollary. Every knot in S³ is concordant to a knot whose exterior is hyperbolic.application/pdfThis material has been previously published. In the Oklahoma State University Library's institutional repository this version is made available through the open access principles and the terms of agreement/consent between the author(s) and the publisher. The permission policy on the use, reproduction or distribution of the material falls under fair use for educational, scholarship, and research purposes. Contact Digital Resources and Discovery Services at lib-dls@okstate.edu or 405-744-9161 for further information.10.1090/S0002-9947-1983-0697074-4Articlenumerical and computational mathematicspure mathematicsmathematical sciencesapplied mathematicsgeneral mathematics3-manifoldhyperbolic 3-manifoldknotlinktanglehomology cobordismknot concordancelink concordanceORCID: 0009-0008-5271-4140 (Myers, R)ScopusID: 7403700679 (Myers, R)1088-6850