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Haefliger proved that there are no smooth j-dimensional knots in <math>S^n</math> provided <math>2n-3j-3>0</math>, and gave further examples of knotted 3-spheres in the 6-sphere.
<math>n-j</math> is called the [[codimension]] of the knot.
Haefliger based his work on Smale's h-cobordism theorem. One of Smale's theorems is that when one deals with knots in co-dimension greater than two, even inequivalent knots have diffeomorphic complements, giving the subject a different flavour than co-dimension 2 knot theory. If one allows topological or PL-isotopies, Zeeman proved that
==See also==
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