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1988•Transactions of the American Mathematical SocietyOpen access

On Aitchison’s construction by isotopy

Daniel S. Silver

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Abstract

We describe a method introduced by I. Aitchison for constructing doubly slice fibered $n$-knots. We prove that all high-dimensional simple doubly slice fibered $n$-knots can be obtained by this construction. (Even-dimensional $n$-knots are required to be $Z$-torsion-free.) We also show that any possible rational Seifert form can be realized by a doubly slice fibered classical knot.

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What this paper is about

We describe a method introduced by I. Aitchison for constructing doubly slice fibered $n$-knots. We prove that all high-dimensional simple doubly slice fibered $n$-knots can be obtained by this construction. (Even-dimensional $n$-knots are required to be $Z$-torsion-free.) We also show that any possible rational Seifert form can be realized by a doubly slice fibered classical knot.

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Available abstract

We describe a method introduced by I. Aitchison for constructing doubly slice fibered $n$-knots. We prove that all high-dimensional simple doubly slice fibered $n$-knots can be obtained by this construction. (Even-dimensional $n$-knots are required to be $Z$-torsion-free.) We also show that any possible rational Seifert form can be realized by a doubly slice fibered classical knot.

Key concepts: Fibered knot, Isotopy, Mathematics, Knot (papermaking), Torsion (gastropod), Pure mathematics, Simple (philosophy), Anatomy

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