On the homotopy of links
Tetsuo Shibuya · Institutional Repositories DataBase (IRDB) · 1988
Let Q be a tame oriented link in a 3-space R 3 .Q is sait to be E-cobordant to a link Q' ( or Q and Q' are E-cobordant ), denoted by Q E Q ', if there are mutuallyand each of m contains a component of Q and one of -Q', where -Q' means the reflective inverse of Q'.(ii) each annulus A of m is non-singular except for finite points P 1 , ... , Pn in the interior of A such that for Bt = N (P;: R 4 ), (aBt, aBt n A) is a Hopf link, [13], where N(x: X) means the regular neighborhood of x in X. m is called E-annuli (between Q and Q').Especially if £-annuli m are level preserving, i.e., m have neither minimal nor maximal points, Q is said to be homotopic to Q' (or Q and Q' are homotopic) and moreover each annulus of SU is non-singular, Q is said to be isotopic to Q' (or Q and Q' are isotopic) and each annulus is non-singular locally flat, Q is said to be ambient isotopic to Q' (or Q and Q' are ambient isotopic) and denoted by Q ~ Q'.