Casson's invariant and twisted double knots

AbstractThis paper presents a formula for Casson's invariant for branched cyclic covers of degree r = ± 1 mod 6 over S3 with branch set a twisted double knot DK. Casson's invariant is compared with the signature of a canonical 4-manifold whose boundary is the branched cyclic cover. For r= −1 mod 6, Casson's invariant is shown to depend upon the knot and the degree of the cover while the signature is independent of the knot in question