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November, 2001 Regenerating Singular Hyperbolic Structures from Sol
Michael Heusener, Joan Porti, Eva Suárez
J. Differential Geom. 59(3): 439-478 (November, 2001). DOI: 10.4310/jdg/1090349448

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.

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Michael Heusener. Joan Porti. Eva Suárez. "Regenerating Singular Hyperbolic Structures from Sol." J. Differential Geom. 59 (3) 439 - 478, November, 2001. https://doi.org/10.4310/jdg/1090349448

Information

Published: November, 2001
First available in Project Euclid: 20 July 2004

zbMATH: 1042.57008
MathSciNet: MR1916952
Digital Object Identifier: 10.4310/jdg/1090349448

Rights: Copyright © 2001 Lehigh University

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Vol.59 • No. 3 • November, 2001
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