Polynomial splittings of Casson-Gordon invariants

Abstract

In this paper we prove that the Casson-Gordon invariants of the connected sum of two knots split when the Alexander polynomials of the knots are coprime. As one application, for any knot K, all but finitely many algebraically slice twisted doubles of K are linearly independent in the knot concordance group.

20 pages, 3 figures; two correct partial forms of Gilmer's theorem included, notational and technical changes made, new Section 5 added