Virtual Knot Groups

Heather A. Dye; Aaron Kaestner

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arXiv · 2110.05613

Virtual Knot Groups

Heather A. Dye·Aaron Kaestner

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Abstract

For a knot diagram $K$, the classical knot group $\pi_1(K)$ is a free group modulo relations determined by Wirtinger-type relations on the classical crossings. The classical knot group is invariant under the Reidemeister moves. In this paper, we define a set of quotient groups associated to a knot diagram $K$. These quotient groups are invariant under the Reidemeister moves and the set includes the extended knot groups defined by Boden et al and Silver and Williams.

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BibTeX RIS

Heather A. Dye, Aaron Kaestner. 2021-10-11. Virtual Knot Groups. https://arxiv.org/abs/2110.05613

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