Abstract
Let M be a torus bundle over S1 with an orientation preserving Anosov monodromy. The manifold M admits a geometric structure modeled on Sol. We prove that the Sol structure can be deformed into singular hyperbolic cone structures whose singular locus Σ ⊂ M is the mapping torus of the fixed point of the monodromy. The hyperbolic cone metrics are parametred by the cone angle α in the interval (0, 2π). When α → 2π, the cone manifolds collapse to the basis of the fibration S1, and they can be rescaled in the direction of the fibers to converge to the Sol manifold. © Applied Probability Trust 2001.
Original language | English |
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Pages (from-to) | 439-478 |
Journal | Journal of Differential Geometry |
Volume | 59 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Jan 2001 |