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Hyperbolic alternating virtual link groups. (English) Zbl 1244.57008
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.

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
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