Farey triangulation
WebJan 10, 2024 · In Section 2 we introduce the Farey words, which represent simple closed curves on the four-times punctured sphere which are not boundary-parallel; the basis of the theory is the relationship between the combinatorics and algebra of these words and the deformations of the curves that they represent. Web杭电上的题虽然多，但是一直苦于找不到问题分类，网页都是英文的，所以平时做题也没怎么看，今天仔细一看，问题分类竟然就在主页。。。。做了那么久的题居然没发现，表示已经狗带。。不要笑，不知道有…
Farey triangulation
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Webthe Farey triangulation: the set of vertices is Q ∪ {1/0}, the set of rational slopes (including 1/0); the edges of C(T) are realized as hyperbolic lines joining Farey neighbors; and the 2-simplices are the ideal triangles of the Farey triangulation. Trivalent tree Σ. The dual graph Σ of C(T) is a trivalent tree embedded Web3.1.Perforated Farey Triangulation To obtain a perforated Farey triangulation, you start with the Farey triangulation of the hyperbolic plane and you add a puncture or a boundary curve to a collection of triangles (see Figures 3 and 4), and so that each arc leaves a puncture or a boundary curve on either side. Figure 3: A perforated Farey ...
WebThe Farey triangulation and thetorus Let H2denote the upper half plane with boundary R. There is a classical ideal triangulation of H2, defined as follows. For any two rational numbers written in lowest terms as p/qand r/s, say they are neighbors if ps−qr = 1. Allow also the case ∞ = 1/0. Webtriangle under this group is the famous Farey tiling. Every edge of the Farey triangulation has a hyperbolic center. This point has the property that hy-perbolic rotation about this …
WebFarey triangulation can be visualized in the disk model of the hyperbolic plane as in Figure 1. Figure 1. The Farey triangulation A horodisk is a disk in H tangent to a boundary point of @H (so it is of in nite radius), and a horocycle is the boundary of a horodisk. A decoration Hof Fis a choice of horocycle tangent to every q2Q^. WebGiven a triangulation, a flip is an operation that consists in switching the diagonals of disjoint quadrilaterals (see Figure 4). These are sometimes referred to as simultaneous flips as opposed ...
WebThere exists an ideal triangulation of the flute surface. Proof. First we take the standard Farey triangulation T of an open disk D. By removing a single point from each triangle …
WebFarey graph and pivot sequence: In Section 2 we discuss the Farey triangu-lation C, a well-known triangulation of the disk with vertices in Qˆ ≡ Q∪{∞}, which can be interpreted in terms of slopes and intersection numbers of simple closed curves on S. The two irrational points ν± determine, via the combina- hoden kostenWebThe triangulation can be naturally embedded in the Farey tessellation. In this section we explain how to extract the triangulation \(\mathbb{T}_{r/s}\) from the Farey tessellation. … hodenmetastasenWebHatcher's perspective is a little bit different from ours, in that he constructs Conway's topograph from the Farey triangulation. However, if you can understand this translation (see pp. 60-61), the discussion on pp. 27-37 is very close to what we are doing in class. hoden lymphabflussWebbending the Farey tessellation, which naturally leads us to discussing kleinian groups and quasi-fuchsian groups. Pushing the bending of the Farey tessellation to the edge of kleinian groups, we reach the fa-mous example associated to the complement of the figure-eight knot. At this point, we are ready to explain that this example is a manifes- hoden leistenkanalWebWe study quasisymmetric maps, which act on the boundary of the hyperbolic plane, by looking at their action on the Farey triangulation. Our main results identify exactly which … hodenkontusionhttp://comet.lehman.cuny.edu/behrstock/seminar/S23/saric.html hodensalatWebbending the Farey tessellation, which naturally leads us to discussing kleinian groups and quasi-fuchsian groups. Pushing the bending of the Farey tessellation to the edge of … hoden peritonealverhältnisse