Titlebook: In the Tradition of Thurston; Geometry and Topolog Ken’ichi Ohshika,Athanase Papadopoulos Book 2020 Springer Nature Switzerland AG 2020 3-m

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Geometry and Topology of Geometric Limits I,c to ..(.) for a finite-type hyperbolic surface .. In the first of the three main theorems which constitute the basic results of this chapter, we construct bi-Lipschitz model manifolds for such hyperbolic 3-manifolds, which have a structure called brick decomposition and are embedded topologically i

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Laminar Groups and 3-Manifolds,ientation-preserving homeomorphisms. This action on the circle is called a universal circle action, due to the rich information it carries. In this chapter, we first review Thurston’s theory of universal circles and follow-up work of other authors. We note that the universal circle action of a 3-man

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Length Functions on Currents and Applications to Dynamics and Counting,cations of length functions to counting problems. Secondly, we use length functions to provide a proof of a folklore theorem which states that pseudo-Anosov homeomorphisms of closed hyperbolic surfaces act on the space of projective geodesic currents with uniform North-South dynamics.

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Signatures of Monic Polynomials,lynomial .. The geometric picture of a monic polynomial is a piecewise smooth planar graph. Smooth isotopy classes relative to the 4. asymptotic ends at infinity of geometric pictures are called signatures. The set of signatures Σ. of monic degree-. polynomials is finite. We give a combinatorial cha

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Quasi-Fuchsian Co-Minkowski Manifolds,sional hyperbolic space. Similarly, since the work of G. Mess, some of these maps can be described using the extrinsic geometry of surfaces in Lorentzian space-forms. Here we will use the degenerate geometry of co-Minkowski space to prove, and generalize to any dimension, a theorem of Thurston that