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On distinguishing virtual knot groups from knot groups. (English) Zbl 1195.57007
The authors give many examples of virtual groups \(G\) which cannot be knots groups. For example by showing that \(H_2(G)\neq 0\), or showing that the group comes from a non-positively, curved square complex, or showing that the group has torsion.
This is hardly surprising as many virtual knots are non-trivial but have trivial group.

57M05 Fundamental group, presentations, free differential calculus
57M50 General geometric structures on low-dimensional manifolds
20F65 Geometric group theory
20F67 Hyperbolic groups and nonpositively curved groups
Full Text: DOI
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