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Transactions of the American Mathematical Society

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The Casson-Gordon invariants in high-dimensional knot theory

Author: Daniel Ruberman
Journal: Trans. Amer. Math. Soc. 306 (1988), 579-595
MSC: Primary 57Q45; Secondary 57M12, 57M25, 57R67
MathSciNet review: 933307
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Abstract: The Casson-Gordon invariants of knots in all dimensions are interpreted in terms of surgery theory. Applications are given to finding non-doubly slice knots, and doubly slice knots which are not the double of a disk knot. In even dimensions, the property of being doubly slice is shown to be largely homotopy theoretic, while in odd dimensions the surgery-theoretic method shows such properties to depend on more than the homotopy type.

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Keywords: Doubly slice knots, surgery groups, $ \alpha $-invariants
Article copyright: © Copyright 1988 American Mathematical Society

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