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Virtual Knot Groups
- Publication Year :
- 2021
-
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.<br />Comment: 12 pages, 13 figures
- Subjects :
- Mathematics - Geometric Topology
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2110.05613
- Document Type :
- Working Paper