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Classical Tessellations and Three-Manifolds

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-d...

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Bibliographic Details
Main Author: Montesinos-Amilibia, José María
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1987, 1987
Edition:1st ed. 1987
Series:Universitext
Subjects:
Complex Manifolds
Chemistry, Physical And Theoretical
Mathematical Methods In Physics
Crystallography And Scattering Methods
Numerical And Computational Physics, Simulation
Manifolds And Cell Complexes (incl. Diff.topology)
Geometry
Physics
Manifolds (mathematics)
Crystallography
Theoretical And Computational Chemistry
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 2.11 The groups
  • 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.
  • 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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