| In this thesis we give examples of (4q + 1)-knots which are doubly sliced but not the double of a disk. The method of detection relies on the Casson-Gordon invariants and a new link invariant.;The link invariant generalizes the Levine-Tristram signatures. From an odd dimensional m component link, L, we obtain a signature function sig(,L): (Q/Z)('m) (--->) Z. This function measures the multiplicity of the various irreducible representations which occur in the G-signature of certain Z(,a(,1)) (CRPLUS) . . . (CRPLUS) Z(,a(,m))-manifolds which we associate to L. It is shown to be an invariant of boundary link cobordism and it is equal to the Levine-Tristram signatures on the diagonal, i.e., sig(,L)((omega), . . . ,(omega)) = (sigma)(,L)((omega)). |
