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140122 ||| eng |
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|a 9783642615726
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|a Montesinos-Amilibia, José María
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|a Classical Tessellations and Three-Manifolds
|h Elektronische Ressource
|c by José María Montesinos-Amilibia
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| 250 |
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|a 1st ed. 1987
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 1987, 1987
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| 300 |
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|a XVII, 230 p. 2 illus
|b online resource
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|a 2.11 The groups
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|a 4.5 The manifolds of euclidean tessellations as Seifert manifolds -- 4.6 The manifolds of spherical tessellations as Seifert manifolds -- 4.7 Involutions on Seifert manifolds -- 4.8 Involutions on the manifolds of tessellations -- Five -- Manifolds of Hyperbolic Tessellations -- 5.1 The hyperbolic tessellations -- 5.2 The groups S?mn, 1/? + 1/m + 1/n < 1 -- 5.3 The manifolds of hyperbolic tessellations -- 5.4 The S1-action -- 5.5 Computing b -- 5.6 Involutions -- Appendix B -- The Hyperbolic Plane -- B.5 Metric -- B.6 The complex projective line -- B.7 The stereographic projection -- B.8 Interpreting G* -- B.10 The parabolic group -- B.11 The elliptic group -- B.12 The hyperbolic group -- Source of the ornaments placed at the end of the chapters -- References -- Further reading -- Notes to Plate I -- Notes to Plate II.
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|a One -- S1-Bundles Over Surfaces -- 1.1 The spherical tangent bundle of the 2-sphere S2 -- 1.2 The S1-bundles of oriented closed surfaces -- 1.3 The Euler number of ST(S2) -- 1.4 The Euler number as a self-intersection number -- 1.5 The Hopf fibration -- 1.6 Description of non-orientable surfaces -- 1.7 S1-bundles over Nk -- 1.8 An illustrative example: IRP2 ? ?P2 -- 1.9 The projective tangent S1-bundles -- Two -- Manifolds of Tessellations on the Euclidean Plane -- 2.1 The manifold of square-tilings -- 2.2 The isometries of the euclidean plane -- 2.3 Interpretation of the manifold of squaretilings -- 2.4 The subgroup ? -- 2.5 The quotient ?\E(2) -- 2.6 The tessellations of the euclidean plane -- 2.7 The manifolds of euclidean tessellations -- 2.8 Involutions in the manifolds of euclidean tessellations -- 2.9 The fundamental groups of the manifolds of euclidean tessellations -- 2.10 Presentations of the fundamental groups of the manifolds M(?) --
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| 653 |
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|a Complex manifolds
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| 653 |
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|a Chemistry, Physical and theoretical
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| 653 |
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|a Mathematical Methods in Physics
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| 653 |
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|a Crystallography and Scattering Methods
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| 653 |
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|a Numerical and Computational Physics, Simulation
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| 653 |
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|a Manifolds and Cell Complexes (incl. Diff.Topology)
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| 653 |
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|a Geometry
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| 653 |
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|a Physics
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| 653 |
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|a Manifolds (Mathematics)
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| 653 |
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|a Crystallography
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| 653 |
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|a Theoretical and Computational Chemistry
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| 653 |
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|a Geometry
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| 041 |
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|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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|a Universitext
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| 856 |
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|u https://doi.org/10.1007/978-3-642-61572-6?nosfx=y
|x Verlag
|3 Volltext
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|a 514.34
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| 520 |
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|a This unusual book, richly illustrated with 29 colour illustrations and about 200 line drawings, explores the relationship between classical tessellations and three-manifolds. In his original and entertaining style, the author provides graduate students with a source of geometrical insight into low-dimensional topology. Researchers in this field will find here an account of a theory that is on the one hand known to them but here is presented in a very different framework
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