相关论文: Negatively Oriented Ideal Triangulations and a Pro…

We study the IR phases of 3D class R theories associated with closed non-hyperbolic 3-manifolds. Non-hyperbolic 3-manifolds can be obtained by performing Dehn fillings on 1-cusped hyperbolic 3-manifolds along exceptional slopes. In 3D-3D…

Let $\Delta$ be a hyperbolic triangle with a fixed area $\varphi$. We prove that for all but countably many $\varphi$, generic choices of $\Delta$ have the property that the group generated by the $\pi$--rotations about the midpoints of the…

We use a variational principle to prove an existence and uniqueness theorem for planar weighted Delaunay triangulations (with non-intersecting site-circles) with prescribed combinatorial type and circle intersection angles. Such weighted…

We give a simple sufficient condition for a spun-normal surface in an ideal triangulation to be incompressible, namely that it is a vertex surface with non-empty boundary which has a quadrilateral in each tetrahedron. While this condition…

We show that the hyperbolic structure on a closed, orientable, hyperbolic 3-manifold can be constructed from a solution to the hyperbolic gluing equations using any triangulation with essential edges. The key ingredients in the proof are…

Previous work of the authors studies minimal triangulations of closed 3-manifolds using a characterisation of low degree edges, embedded layered solid torus subcomplexes and 1-dimensional $\mathbb{Z}_2$-cohomology. The underlying blueprint…

We introduce a construction that simultaneously yields cusped spaces of relatively hyperbolic groups, and spaces quasi-isometric to Teichmueller metrics. We use this to study Dehn-filling-like quotients of various groups, among which…

We define a new condition on relatively hyperbolic Dehn filling which allows us to control the behavior of a relatively quasiconvex subgroups which need not be full. As an application, in combination with a recent result of Cooper and…

Thurston's circle packing approximation of the Riemann Mapping (proven to give the Riemann Mapping in the limit by Rodin-Sullivan) is largely based on the theorem that any topological disk with a circle packing metric can be deformed into a…

We develop a Thurston-like theory to characterize geometrically finite rational maps, then apply it to study pinching and plumbing deformations of rational maps. We show that in certain conditions the pinching path converges uniformly and…

Given a fibred hyperbolic 3-manifold with boundary, we coarsely relate the Euclidean geometry of its cusps to the classical fractional Dehn twist coefficient of its monodromy. This result fits into the broader programme of coarsely…

This paper illustrates a computational approach to Culler-Morgan-Shalen theory using ideal triangulations, spun-normal surfaces and tropical geometry. Certain affine algebraic sets associated to the Whitehead link complement as well as…

We establish a connection between two previously unrelated topics: a particular discrete version of conformal geometry for triangulated surfaces, and the geometry of ideal polyhedra in hyperbolic three-space. Two triangulated surfaces are…

We propose a new algorithm for Dehn surgery problem, finding exceptional Dehn filling slopes for a given hyperbolic 3-manifold with a torus boundary, using a quantum invariant called "3D index". The invariant is defined using an ideal…

Following the approach of Dahmani, Guirardel and Osin, we extend the group theoretical Dehn filling theorem to show that the pre-images of infinite order elements have a certain structure of a free product. We then apply this result to show…

We explicitly describe the Teichmuller space TH_n of hyperelliptic surfaces in terms of natural and effective coordinates as the space of certain (2n-6)-tuples of distinct points on the ideal boundary of the Poincare disc. We essentially…

In this paper, we determine the canonical polyhedral decomposition of every hyperbolic once-punctured torus bundle over the circle. In fact, we show that the only ideal polyhedral decomposition that is straight in the hyperbolic structure…

This paper concerns with a rigidity of core geodesics in hyperbolic Dehn fillings. For instance, for an $n$-cusped hyperbolic $3$-manifold $M$ having non-symmetric cusp shapes, we show any Dehn filling of $M$ with sufficiently large…

In \cite{confol} Y. Eliashberg and W. Thurston gave a definition of tight confoliations. We give an example of a tight confoliation $\xi$ on $T^3$ violating the Thurston-Bennequin inequalities. This answers a question from \cite{confol}…

In this paper we provide a computer assisted proof that about two thousand surgeries far away from the ideal point in the hyperbolic Dehn filling space of the figure-eight knot complement are infinitesimally projectively rigid. We also…