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Discriminants of Casson–Gordon invariants

Published online by Cambridge University Press:  24 October 2008

Patrick Gilmer  and
Charles Livingston
Patrick Gilmer
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.
Charles Livingston
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A.
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Extract

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(ℚ(ζd)(t)) ⊗ ℚ; here ζd denotes a primitive dth root of unity. Litherland [20] observed that one could usually tensor with ℤ(2) instead of ℚ, 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(ℚ(ζd)) ⊗ ℤ(2) modulo the image of L0(ℚ(ζd)) ⊗ ℤ(2).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 1 , July 1992 , pp. 127 - 139
Copyright
Copyright © Cambridge Philosophical Society 1992

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