Regenerating singular hyperbolic structures from Sol

Michael Heusener, Joan Porti, Eva Suárez

Research output: Contribution to journalArticleResearchpeer-review

8 Citations (Scopus)

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 languageEnglish
Pages (from-to)439-478
JournalJournal of Differential Geometry
Volume59
Issue number3
DOIs
Publication statusPublished - 1 Jan 2001

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