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| == Flat surfaces in Sage == | #REDIRECT dynamics/FlatSurfaces = Flat surfaces = |
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| === Introduction === For general mathematic references see the [[https://lma.homelinux.org/wiki/FlatSurfaces/FlatSurfaces|Flat surfaces wiki]]. A flat surfaces can be seen either * as a union of polygons glued along pairs of parallel sides, * as a flat metric with no holonomy on a surface, * as a Riemann surface and a non zero Abelian (or quadratic) differential. This page is aimed to be a roadmap for the implementations of various algorithm related to flat surfaces and more generally geometry of surfaces. === Different representations/implementations for flat surfaces === * (convex) polygonal surface * rectangulated surface * suspension of iet (and li) (almost in Sage) * Thurston-Veech construction * triangulated surface * Delaunay surface (?) * Algebraic curve with Abelian or quadratic differential * Coverings (make it relative)... need to implement maps between translation surfaces * square tiled surfaces/origamis (covering of the torus) (almost in Sage) * hyperelliptic curves (specifying the double cover over the sphere) * Unfoldings of rational billiards === Needed generic methods === * switch between representations (the one where everybody can be converted is triangulated flat surface) * computing fundamental group and homology * maps between flat surfaces * action of SL(2,R) and isomorphisms === Hyperbolic geometry === * the three 2D models: hyperbolic plane '''HH''', hyperbolic disc '''DD''' and the hyperboloïd * polygonal domains * tesselations (covering of HH by finite area convex polygonal domains) * Fuchsian groups and fundamental domains |
This page has moved to [[dynamics/FlatSurfaces]] |
