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arXiv · 2003.00512

A geometric invariant of virtual n-links

Blake K Winter
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Abstract

For a virtual $n$-link $K$, we define a new virtual link $VD(K)$, which is invariant under virtual equivalence of $K$. The Dehn space of $VD(K)$, which we denote $DD(K)$, therefore has a homotopy type which is an invariant of $K$. We show that the quandle and even the fundamental group of this space are able to detect the virtual trefoil. We also consider applications to higher-dimensional virtual links.

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Blake K Winter. 2020-03-01. A geometric invariant of virtual n-links. https://arxiv.org/abs/2003.00512

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