On signature invariants of links

Abstract

Theory of signature invariants of links in rational homology spheres is developed. The signature is defined via complexity and Seifert matrix over Q and shown to be link concordance invariant with standard properties of usual link signature. As an application Cochran-Orr``s answer to the long-standing question that whether all links are concordant to boundary links is obtained again. Casson-Gordan invariants for specific branched covers of links are investigated to obtain slice obstruction and boundary link concordance invariant. A method to calculate the invariants from Seifert matrices and voltage assignments is suggested and some examples are illustrated.