Abstract
We work in the smooth category. An (oriented) (ordered) m-component n-(dimensional) link is a smooth oriented submanifold L = {K1, …, Km} of Sn+2 which is the ordered disjoint union of m manifolds, each PL-homeomorphic to the standard n-sphere. If m = 1, then L is called a knot. We say that m-component n-dimensional links L0 and L1 are (link-)concordant or (link-)cobordant if there is a smooth oriented submanifold C = {C1, …, Cm} of Sn+2 × [0, 1] which meets the boundary transversely in ∂C, is PL-homeomorphic to L0 × [0, 1], and meets Sn+2 × {l} in Ll (l = 0, 1). If m = 1, then we say that n-knots L0 and Ll are (knot-)concordant or (knot-)cobordant. Then we call C a concordance-cylinder of the two n-knots L0 and Ll. If an n-link L is concordant to the trivial link, then we call L a slice link. If an n-link L = {K1, …, Km} ⊂ Sn+2 = ∂Bn+3 ⊂ Bn+3 is slice, then there is a disjoint union of (n + 1)-discs D 1 n + 1 II ··· II D m n + 1 in Bn+3 such that D 1 n + 1 ∩ S n + 2 = ∂ D i n + 1 = K i . ( D 1 n + 1 , … , D m n + 1 ) is called a set of slice discs for L. If m = 1, then D 1 n + 1 is called a slice disc for the knot L. 1991 Mathematics Subject Classification 57M25, 57Q45.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
