Harlander, Jens; Rosebrock, Stephan On distinguishing virtual knot groups from knot groups. (English) Zbl 1195.57007 J. Knot Theory Ramifications 19, No. 5, 695-704 (2010). 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. Reviewer: Roger Fenn (Brighton) Cited in 1 Document MSC: 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 Keywords:virtual knots; Wirtinger presentation; knot groups; non-positively curved square-complex PDFBibTeX XMLCite \textit{J. Harlander} and \textit{S. Rosebrock}, J. Knot Theory Ramifications 19, No. 5, 695--704 (2010; Zbl 1195.57007) Full Text: DOI References: [1] DOI: 10.1007/978-3-662-12494-9 · doi:10.1007/978-3-662-12494-9 [2] Bogley W. A., LMS Lecture Note Series 197, in: Two-dimensional Homotopy and Combinatorial Group Theory (1993) [3] Burde G., de Gruyter Studies in Mathematics, in: Knots (2003) [4] Carter J. S., Mathematical Surveys and Monographs 55, in: Knotted Surfaces and Their Diagrams (1998) · Zbl 0904.57010 [5] DOI: 10.2140/agt.2005.5.509 · Zbl 1083.57007 · doi:10.2140/agt.2005.5.509 [6] DOI: 10.4064/fm188-0-13 · Zbl 1084.57005 · doi:10.4064/fm188-0-13 [7] DOI: 10.1142/S0218216503002871 · Zbl 1053.57005 · doi:10.1142/S0218216503002871 [8] DOI: 10.1007/BF02571435 · Zbl 0761.57003 · doi:10.1007/BF02571435 [9] Huck G., Proc. Edinburgh Math. Soc. A 137 pp 519– · Zbl 1134.57002 · doi:10.1017/S0308210505000053 [10] DOI: 10.1006/eujc.1999.0314 · Zbl 0938.57006 · doi:10.1006/eujc.1999.0314 [11] DOI: 10.1007/978-3-642-61896-3 · doi:10.1007/978-3-642-61896-3 [12] DOI: 10.2307/1970113 · Zbl 0078.16402 · doi:10.2307/1970113 [13] DOI: 10.1142/S0218216594000162 · Zbl 0824.57005 · doi:10.1142/S0218216594000162 [14] Rosebrock S., Siberian Electron. Math. Rep. 4 pp 440– [15] Satoh S., J. Knot Theory Ramifications 9 pp 531– This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.