Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Discriminants of Casson–Gordon invariants

Patrick Gilmera1 and Charles Livingstona2

a1 Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.

a2 Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A.

Casson–Gordon invariants were first used to prove that certain algebraically slice knots in S3 are not slice knots [2, 3]. Since then they have been applied to a wide range of problems, including embedding problems and questions relating to boundary links [2, 10, 21, 25]. The most general Casson–Gordon invariant takes its value in L0(xs211Ad)(t)) xs2297 xs211A; here ζd denotes a primitive dth root of unity. Litherland [20] observed that one could usually tensor with ℤ(2) instead of xs211A, and in this way preserve the 2-torsion in the Witt group. He then constructed new examples of non-slice genus two knots which were detected with torsion classes in L0(xs211Ad)) xs2297(2) modulo the image of L0(xs211Ad)) xs2297(2).

(Received May 13 1991)