Mathematical Proceedings of the Cambridge Philosophical Society



Polynomial splittings of Casson–Gordon invariants


SE-GOO KIM a1
a1 Department of Mathematics, University of California, Santa Barbara, CA 93106, U.S.A. e-mail: sekim@math.ucsb.edu

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Abstract

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.

(Received September 16 2003)
(Revised October 28 2003)