Classification of simple knots by Blanchfield duality

Abstract

The purpose of this paper is to announce some results on simple knots, i.e. knots of S 2q ~l in S 2q + 1 whose complements have the homotopy (q -l)-type of S 1 . We state in 4 two theorems proved in the author's Ph.D. thesis These results are proved using a generalization of the presentation method for classical knots.