CAT(0) structures on virtual and alternating knot complements
by Iain Aitchison
Abstract: Knot theory can be developed in Euclidean space or in the 3-sphere. Complete hyperbolic structures exist on the complements of many links in the 3-sphere, but cannot exist on the complement of a knot in Euclidean space. We show that for the class of
prime, non-split alternating knots, a complete CAT(0) structure can be defined naturally on the complement in either ambient space. This construction generalizes to so-called virtual knots and links. The basic notions will be given, and the construction described.
This is joint work with Lawrence Reeves.
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