The triviality of a certain invariant of link maps in the four-sphere

Ash Lightfoot

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arXiv · 1609.06166

The triviality of a certain invariant of link maps in the four-sphere

Ash Lightfoot

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Abstract

It is an open problem whether Kirk's $\sigma$ invariant is the complete obstruction to a link map $S^2\cup S^2\to S^4$ being link homotopically trivial. With the objective of constructing counterexamples, Li proposed a link homotopy invariant $\omega$ that is defined on the kernel of $\sigma$ and also obstructs link nullhomotopy. We show that $\omega$ is determined by $\sigma$, and is a strictly weaker invariant.

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Ash Lightfoot. 2016-09-20. The triviality of a certain invariant of link maps in the four-sphere. https://arxiv.org/abs/1609.06166

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