Cylinder decomposition veech surface
WebA Veech surface (X,q) is called primitive if it cannot be realized as a branched cover over (X′,q′), where the genus of X′ is lower than the genus of X and the quadratic differential q′ pulls back to q under the covering map. If (X,q) is a Veech surface that is not primitive, then the corresponding surface (X′,q′) is also Veech WebJun 18, 2024 · In the first case, there is only one cylinder decomposition because any other decomposition would contain a closed geodesic that would cross every cylinder …
Cylinder decomposition veech surface
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WebMore precisely, regular n-gon surfaces have (n, ∞, ∞)-triangle groups as Veech groups, while the Veech groups of Bouw-Möller surfaces are (m, n, ∞)-triangle groups for m and n not both even ... http://www-personal.umich.edu/~alexmw/Cylinder.pdf
WebA cylinder diagram encodes the combinatorics of cylinder decomposition of a completely periodic direction in a translation surface. If we adjoin coordinates to this combinatorial datum, we have a complete description of the underlying surface. In the case of arithmetic curves, the coordinates can be taken to be rational numbers. WebA Veech surface is arithmeticif it is a covering of a flat torus, ramified over one point; otherwise, it is a non-arithmetic Veech surface. 2.2. Classification of Veech surfaces …
Webclosure of a translation surface and the cylinders on the translation surface. The Siegel-Veech formula establishes such a connection asymp-totically in counting problems [Vee98,EM01]. The Veech Dichotomy shows in particular that for translation surfaces in closed orbits, a very strong form of complete peri-odicity holds [Vee89]. Webbecause a surface in a fixed stratum can have arbitrarily many short saddle connections (for instance, by taking a surface with a short slit, and then gluing in a cylinder with small height and circumference). But, according to Theorem 1.2, as we increase R, the effect of these short saddle connections eventually diminishes.
WebThe Veech group of the surface is the subgroup of SL(2,R) consisting of elements that map the surface to itself by this action. I will describe a method for computing elements of the Veech group. ... • A multi-curve on a surface produces a decomposition of the surface into cylinders. Thus a parabolic automorphism of the surface may be ...
Webdecomposes into cylinders in that direction and a surface (X,ω) is said to be completely periodic, if any direction that has some cylinder in that direction is completely periodic. Calta ([Ca]) showed that in genus 2, if the holonomy field lies in a quadratic extension of Q, then if the surface is not a Veech surface, it is completely periodic. fanfiction cloud 4012http://homepages.math.uic.edu/~masur/chm-rv.pdf fanfiction citrus scaleWebAug 28, 2024 · Figure 12. A cylinder decomposition of the surface of genus $ 2 $ Figure 13. A dilation torus, which is not a Hopf torus Figure 14. A dilation surface with a non-discrete set of holonomy vectors of saddle connections starting at the black point Figure 15. An angular section in which all leaves are hyperbolic Figure 16. cork sole slippers productWebsuch a cylinder never exits it which is incompatible with the fact that a trian-gulated surface deprived of its 1-skeleton is a union of triangles. A remarkable … fanfiction chicago pd antonio hurthttp://homepages.math.uic.edu/~masur/chm.pdf fanfiction circus baby balloonWebDec 19, 2016 · Theorem 1.1. Let S be a Veech surface in 7i(2) which cannot be rescaled so that p(Hi(S,Z)) cQxQ. Let v be a completely periodic direction for S. Suppose the cylinder decompositon in the direction v has two cylinders. Let Wi,w2,hi,h2,ti,t2 be the widths, heights and twists of these two cylinders. The twists are measured corksol halifaxWebSurface Area of Cylinder. The amount of square units required to cover the surface of the cylinder is the surface area of the cylinder. The formula for the surface area of the cylinder is equal to the total surface area of the … fanfiction clexa youre the only love