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- Fuchsian_group abstract "In mathematics, a Fuchsian group is a discrete subgroup of PSL(2,R). The group PSL(2,R) can be regarded as a group of isometries of the hyperbolic plane, or conformal transformations of the unit disc, or conformal transformations of the upper half plane, so a Fuchsian group can be regarded as a group acting on any of these spaces. There are some variations of the definition: sometimes the Fuchsian group is assumed to be finitely generated, sometimes it is allowed to be a subgroup of PGL(2,R) = PSL(2,R).2 (so that it contains orientation-reversing elements) and sometimes it is allowed to be a Kleinian group (a discrete group of PSL(2,C)) that is conjugate to a subgroup of PSL(2,R).Fuchsian groups are used to create Fuchsian models of Riemann surfaces. In this case, the group may be called the Fuchsian group of the surface. In some sense, Fuchsian groups do for non-Euclidean geometry what crystallographic groups do for Euclidean geometry. Some Escher graphics are based on them (for the disc model of hyperbolic geometry).General Fuchsian groups were first studied by Poincaré (1882), who was motivated by the paper (Fuchs 1880) and therefore named them after Lazarus Fuchs.".
- Fuchsian_group wikiPageExternalLink purl?PPN243919689_0089.
- Fuchsian_group wikiPageID "471365".
- Fuchsian_group wikiPageLength "10275".
- Fuchsian_group wikiPageOutDegree "72".
- Fuchsian_group wikiPageRevisionID "675189620".
- Fuchsian_group wikiPageWikiLink (2,3,7)_triangle_group.
- Fuchsian_group wikiPageWikiLink Abelian_group.
- Fuchsian_group wikiPageWikiLink Acta_Mathematica.
- Fuchsian_group wikiPageWikiLink Cantor_set.
- Fuchsian_group wikiPageWikiLink Category:Discrete_groups.
- Fuchsian_group wikiPageWikiLink Category:Fractals.
- Fuchsian_group wikiPageWikiLink Category:Hyperbolic_geometry.
- Fuchsian_group wikiPageWikiLink Category:Kleinian_groups.
- Fuchsian_group wikiPageWikiLink Category:Riemann_surfaces.
- Fuchsian_group wikiPageWikiLink Centralizer_and_normalizer.
- Fuchsian_group wikiPageWikiLink David_Mumford.
- Fuchsian_group wikiPageWikiLink Dense_set.
- Fuchsian_group wikiPageWikiLink Discrete_group.
- Fuchsian_group wikiPageWikiLink Elliptic_curve.
- Fuchsian_group wikiPageWikiLink Euclidean_geometry.
- Fuchsian_group wikiPageWikiLink Fuchsian_model.
- Fuchsian_group wikiPageWikiLink Graduate_Studies_in_Mathematics.
- Fuchsian_group wikiPageWikiLink Group_(mathematics).
- Fuchsian_group wikiPageWikiLink Group_action.
- Fuchsian_group wikiPageWikiLink Henryk_Iwaniec.
- Fuchsian_group wikiPageWikiLink Hurwitzs_automorphisms_theorem.
- Fuchsian_group wikiPageWikiLink Hyperbolic_geometry.
- Fuchsian_group wikiPageWikiLink Hyperbolic_space.
- Fuchsian_group wikiPageWikiLink Indras_Pearls_(book).
- Fuchsian_group wikiPageWikiLink Isometry.
- Fuchsian_group wikiPageWikiLink Klein_quartic.
- Fuchsian_group wikiPageWikiLink Kleinian_group.
- Fuchsian_group wikiPageWikiLink Lazarus_Fuchs.
- Fuchsian_group wikiPageWikiLink Limit_point.
- Fuchsian_group wikiPageWikiLink Limit_set.
- Fuchsian_group wikiPageWikiLink Linear_fractional_transformation.
- Fuchsian_group wikiPageWikiLink M._C._Escher.
- Fuchsian_group wikiPageWikiLink Macbeath_surface.
- Fuchsian_group wikiPageWikiLink Mathematics.
- Fuchsian_group wikiPageWikiLink Modular_group.
- Fuchsian_group wikiPageWikiLink Moduli_space.
- Fuchsian_group wikiPageWikiLink Möbius_transformation.
- Fuchsian_group wikiPageWikiLink Non-Euclidean_crystallographic_group.
- Fuchsian_group wikiPageWikiLink Non-Euclidean_geometry.
- Fuchsian_group wikiPageWikiLink Nowhere_dense_set.
- Fuchsian_group wikiPageWikiLink Open_set.
- Fuchsian_group wikiPageWikiLink Orientability.
- Fuchsian_group wikiPageWikiLink Perfect_set.
- Fuchsian_group wikiPageWikiLink Quasi-Fuchsian_group.
- Fuchsian_group wikiPageWikiLink Rational_number.
- Fuchsian_group wikiPageWikiLink Region_of_discontinuity.
- Fuchsian_group wikiPageWikiLink Riemann_sphere.
- Fuchsian_group wikiPageWikiLink Riemann_surface.
- Fuchsian_group wikiPageWikiLink SL2(R).
- Fuchsian_group wikiPageWikiLink Schottky_group.
- Fuchsian_group wikiPageWikiLink Space_group.
- Fuchsian_group wikiPageWikiLink Svetlana_Katok.
- Fuchsian_group wikiPageWikiLink Systolic_geometry.
- Fuchsian_group wikiPageWikiLink Triangle_group.
- Fuchsian_group wikiPageWikiLink Unit_disk.
- Fuchsian_group wikiPageWikiLink Upper_half-plane.
- Fuchsian_group wikiPageWikiLinkText "Fuchsian group".
- Fuchsian_group first "E. B.".
- Fuchsian_group id "F/f041890".
- Fuchsian_group last "Vinberg".
- Fuchsian_group wikiPageUsesTemplate Template:Citation.
- Fuchsian_group wikiPageUsesTemplate Template:Harvard_citation.
- Fuchsian_group wikiPageUsesTemplate Template:Harvard_citation_text.
- Fuchsian_group wikiPageUsesTemplate Template:Springer.
- Fuchsian_group subject Category:Discrete_groups.
- Fuchsian_group subject Category:Fractals.
- Fuchsian_group subject Category:Hyperbolic_geometry.
- Fuchsian_group subject Category:Kleinian_groups.
- Fuchsian_group subject Category:Riemann_surfaces.
- Fuchsian_group hypernym Subgroup.
- Fuchsian_group type EthnicGroup.
- Fuchsian_group type Group.
- Fuchsian_group type Function.
- Fuchsian_group type Group.
- Fuchsian_group type Surface.
- Fuchsian_group comment "In mathematics, a Fuchsian group is a discrete subgroup of PSL(2,R). The group PSL(2,R) can be regarded as a group of isometries of the hyperbolic plane, or conformal transformations of the unit disc, or conformal transformations of the upper half plane, so a Fuchsian group can be regarded as a group acting on any of these spaces.".
- Fuchsian_group label "Fuchsian group".
- Fuchsian_group sameAs Q205124.
- Fuchsian_group sameAs Fuchssche_Gruppe.
- Fuchsian_group sameAs گروه_فوکسی.
- Fuchsian_group sameAs Gruppo_fuchsiano.
- Fuchsian_group sameAs 푹스_군.
- Fuchsian_group sameAs Fuchs-groep.
- Fuchsian_group sameAs Grupo_fuchsiano.
- Fuchsian_group sameAs m.02dj59.
- Fuchsian_group sameAs Q205124.
- Fuchsian_group wasDerivedFrom Fuchsian_group?oldid=675189620.
- Fuchsian_group isPrimaryTopicOf Fuchsian_group.