The Complexity of Shake Slice Knots

Charles Ransome Stine

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arXiv · 2111.12666

The Complexity of Shake Slice Knots

Charles Ransome Stine

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Abstract

We define a notion of complexity for shake-slice knots which is analogous to the definition of complexity for h-cobordisms studied by Morgan-Szab\'o. We prove that for each framing $n \ne 0$ and complexity $c \ge 0$, there is an $n$-shake-slice knot with complexity at least $c$. Our construction makes use of dualizable patterns, and we include a crash course in their properties. We bound complexity by studying the behavior of the classical knot signature and the Levine-Tristram signature of a knot under the operation of twisting algebraically-one strands.

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Charles Ransome Stine. 2021-11-24. The Complexity of Shake Slice Knots. https://arxiv.org/abs/2111.12666

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