Some 4-manifold geometry from hyperbolic knots in S^3
  A 4-manifold is constructed with some curious metric properties; or maybe it is many 4-manifolds masquerading as one, which would explain why it looks curious. Anyway, knots in the 3-sphere with complete finite volume hyperbolic metrics on their complements play a role in this story. 
Clifford Henry Taubes
math.DG math.GT