Homology cobordisms, link concordances, and hyperbolic -manifolds

Author:
Robert Myers

Journal:
Trans. Amer. Math. Soc. **278** (1983), 271-288

MSC:
Primary 57N10; Secondary 57M40, 57N70

DOI:
https://doi.org/10.1090/S0002-9947-1983-0697074-4

MathSciNet review:
697074

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Abstract | References | Similar Articles | Additional Information

Abstract: Let and be compact, oriented -manifolds. They are *homology cobordant* (respectively *relative homology cobordant*) if and there is a smooth, compact oriented -manifold such that (resp. and are isomorphisms, .

Theorem. *Every closed, oriented* -*manifold is homology cobordant to a hyperbolic* -*manifold*.

Theorem. *Every compact, oriented* -*manifold whose boundary is nonempty and contains no* -*spheres is relative homology cobordant to a hyperbolic* -*manifold*.

Two oriented links and in a -manifold are *concordant* if there is a set of smooth, disjoint, oriented annuli in such that , where .

Theorem. *Every link in a compact, oriented* -*manifold* *whose boundary contains no* -*spheres is concordant to a link whose exterior is hyperbolic*.

Corollary. *Every knot in* *is concordant to a knot whose exterior is hyperbolic*.

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DOI:
https://doi.org/10.1090/S0002-9947-1983-0697074-4

Keywords:
-manifold,
hyperbolic -manifold,
knot,
link,
tangle,
homology cobordism,
knot concordance,
link concordance

Article copyright:
© Copyright 1983
American Mathematical Society