Classical Tessellations and Three-Manifolds (Universitext) de José María Montesinos-Amilibia

Classical Tessellations and Three-Manifolds: Universitext

José María Montesinos-Amilibia

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 "clothed in a different garb" and can be used as a source for seminars on low-dimensional topology, or for preparing independent study projects for students, or again as the basis of a reading course.

Citește tot Restrânge

Din seria Universitext

17%

Preț: 361^.79 lei
15%

Preț: 532^.79 lei
15%

Preț: 542^.16 lei
15%

Preț: 499^.29 lei
17%

Preț: 427^.29 lei
17%

Preț: 364^.55 lei
17%

Preț: 365^.99 lei
14%

Preț: 392^.36 lei
Preț: 659^.84 lei
15%

Preț: 484^.28 lei
Preț: 351^.26 lei
17%

Preț: 431^.47 lei
Preț: 379^.22 lei
19%

Preț: 393^.94 lei
Preț: 396^.88 lei
Preț: 374^.66 lei
13%

Preț: 358^.07 lei
17%

Preț: 364^.80 lei
Preț: 356^.91 lei
17%

Preț: 426^.75 lei
Preț: 621^.58 lei
Preț: 478^.13 lei
17%

Preț: 427^.65 lei
20%

Preț: 569^.53 lei
15%

Preț: 722^.54 lei
17%

Preț: 369^.05 lei
14%

Preț: 352^.81 lei
17%

Preț: 394^.40 lei
Preț: 375^.53 lei
Preț: 269^.56 lei
Preț: 372^.24 lei
Preț: 436^.91 lei
Preț: 374^.69 lei
15%

Preț: 522^.94 lei
15%

Preț: 486^.00 lei
15%

Preț: 465^.23 lei
Preț: 381^.87 lei
Preț: 474^.35 lei
15%

Preț: 630^.46 lei
Preț: 406^.68 lei
15%

Preț: 590^.07 lei
20%

Preț: 499^.94 lei
15%

Preț: 576^.47 lei
Preț: 373^.94 lei
Preț: 479^.99 lei
Preț: 483^.95 lei
20%

Preț: 325^.56 lei
15%

Preț: 463^.79 lei
Preț: 451^.62 lei

Cuprins

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.

Textul de pe ultima copertă