Cylinder decomposition veech surface
WebAug 17, 2004 · the direction v, the surface decomposes as a union of cylinders. A surface S is completely periodic if any direction in which there is at least one cylinder of closed … 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.
Cylinder decomposition veech surface
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WebThe trace eld of a Veech surface (X;!) is Q(tr A : A 2SL(X;!)) is the smallest eld extension of Q that contains the trace of all elements of SL(X;!). 1 For an appropriately scaled … http://www-personal.umich.edu/~alexmw/Cylinder.pdf
WebDownload scientific diagram Cylinder decomposition of the double pentagon surface. One cylinder is white; the other is shaded from publication: Cutting sequences, regular polygons, and the Veech ... WebAmerican Mathematical Society :: Homepage
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. WebAug 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 …
WebJun 18, 2024 · Theorem 1.2 is proved in Sect. 3. Horizon saddle connections constrain the action of \(SL(2,\mathbb {R})\).In the following, the Veech group V(X) of a dilation surface X is the stabilizer of the action of \(SL(2,\mathbb {R})\).There is a remarkable similarity with the three types of Veech groups for translation surfaces with poles: continuous, cyclic …
Webcylinders of height and width (h 1,w 1) and (h 2,w 2), see Figure 1.1.4. On each cylinder we can define a Dehn twist via (x,y) 7→(x,y+µ−1xmod h), where following tradition, the … derili bali tour officeWebA 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. chronic scarring in lungsWebThe non-Veech case of Theorem1.2is proved very similarly to Theorem1.1. Finally we have some additional results on polygonal area when q is a Veech surface. The first of these will be derived from the analogous result for VT(q) in [SW10]. Theorem1.3. If q is a Veech surface then Poly(q) is a discrete subset of R. Next, for a ¨0 define the ... chronic schizophrenia icd 10WebMore 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 ... chronic schizoaffective disorder icd 10WebA 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 … chronic scapholunate injuryWebAug 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. chronic schmorl\u0027s node in spineWebThe proofs combine recent results on Masur–Veech volumes of moduli spaces of meromorphic quadratic differentials in genus zero with our new observation that horizontal and vertical separatrix diagrams of integer quadratic … chronic schizoaffective disorder icd 10 code