an:06019680
Zbl 1244.57008
Harlander, Jens
Hyperbolic alternating virtual link groups
EN
Groups Geom. Dyn. 6, No. 1, 83-96 (2012).
00296683
2012
j
57M05 57M50 20F65 20F67
alternating virtual knot; hyperbolic group; Wirtinger complex; non-positively curved square complex
The article under review studies the geometry of certain link complements. The author identifies two types of forbidden tangles and proves that if a prime, alternating link projection does not contain either of those two tangles then the fundamental group \(G\) of the complement is the fundamental group of a finite, piecewise Euclidean 2-complex of nonpositive curvature. If one assumes that the link projection is dense, then \(G\) is shown to be hyperbolic.
Thomas Koberda (Cambridge)