Link homotopic but not isotopic

Abstract

Given an $m$-component link $L$ in $S^3$ ($m\ge 2$), we construct a family of links which are link homotopic, but not link isotopic, to $L$. Every proper sublink of such a link is link isotopic to the corresponding sublink of $L$. Moreover, if $L$ is an unlink then there exist links that in addition to the above properties have all Milnor invariants zero.

arXiv comment16 pages, 24 figures

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