José María Montesinos-Amilibia
Classical Tessellations and Three-Manifolds (eBook, PDF)
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José María Montesinos-Amilibia
Classical Tessellations and Three-Manifolds (eBook, PDF)
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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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- Größe: 13.72MB
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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.
Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.
Produktdetails
- Produktdetails
- Verlag: Springer Berlin Heidelberg
- Seitenzahl: 230
- Erscheinungstermin: 6. Dezember 2012
- Englisch
- ISBN-13: 9783642615726
- Artikelnr.: 53139058
- Verlag: Springer Berlin Heidelberg
- Seitenzahl: 230
- Erscheinungstermin: 6. Dezember 2012
- Englisch
- ISBN-13: 9783642615726
- Artikelnr.: 53139058
- Herstellerkennzeichnung Die Herstellerinformationen sind derzeit nicht verfügbar.
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(?).- 2.11 The groups $$ tilde Gamma $$ as 3-dimensional crystallographic groups.- Appendix A.- Orbifolds.- Three.- Manifolds of Spherical Tessellations.- 3.1 The isometries of the 2-sphere.- 3.2 The fundamental group of SO(3).- 3.3 Review of quaternions.- 3.4 Right-helix turns.- 3.5 Left-helix turns.- 3.6 The universal cover of SO(4).- 3.7 The finite subgroups of SO(3).- 3.8 The finite subgroups of the quaternions.- 3.9 Description of the manifolds of tessellations.- 3.10 Prism manifolds.- 3.11 The octahedral space.- 3.12 The truncated-cube space.- 3.13 The dodecahedral space.- 3.14 Exercises on coverings.- 3.15 Involutions in the manifolds of spherical tessellations.- 3.16 The groups $$ tilde Gamma $$ as groups of tessellations of S3.- Four.- Seifert Manifolds.- 4.1 Definition.- 4.2 Invariants.- 4.3 Constructing the manifold from the invariants.- 4.4 Change of orientation and normalization.- 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.Contents: S1-Bundles Over Surfaces.- Manifolds of Tessellations on the Euclidean Plane.- Appendix A: Orbifolds.- Manifolds of Spherical Tessellations.- Seifert Manifolds.- Manifolds of Hyperbolic Tessellations.- Appendix B: The Hyperbolic Plane.- Source of the Ornaments.- 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(?).- 2.11 The groups $$ tilde Gamma $$ as 3-dimensional crystallographic groups.- Appendix A.- Orbifolds.- Three.- Manifolds of Spherical Tessellations.- 3.1 The isometries of the 2-sphere.- 3.2 The fundamental group of SO(3).- 3.3 Review of quaternions.- 3.4 Right-helix turns.- 3.5 Left-helix turns.- 3.6 The universal cover of SO(4).- 3.7 The finite subgroups of SO(3).- 3.8 The finite subgroups of the quaternions.- 3.9 Description of the manifolds of tessellations.- 3.10 Prism manifolds.- 3.11 The octahedral space.- 3.12 The truncated-cube space.- 3.13 The dodecahedral space.- 3.14 Exercises on coverings.- 3.15 Involutions in the manifolds of spherical tessellations.- 3.16 The groups $$ tilde Gamma $$ as groups of tessellations of S3.- Four.- Seifert Manifolds.- 4.1 Definition.- 4.2 Invariants.- 4.3 Constructing the manifold from the invariants.- 4.4 Change of orientation and normalization.- 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.Contents: S1-Bundles Over Surfaces.- Manifolds of Tessellations on the Euclidean Plane.- Appendix A: Orbifolds.- Manifolds of Spherical Tessellations.- Seifert Manifolds.- Manifolds of Hyperbolic Tessellations.- Appendix B: The Hyperbolic Plane.- Source of the Ornaments.- References.- Further Reading.- Notes to Plate I.- Notes to Plate II.