Buch, Englisch, Band 484, 277 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1300 g
Buch, Englisch, Band 484, 277 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1300 g
Reihe: Mathematics and its Applications
ISBN: 978-0-7923-5767-4
Verlag: Springer Netherlands
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
- Mathematik | Informatik Mathematik Topologie Analytische Topologie
- Mathematik | Informatik Mathematik Topologie Algebraische Topologie
- Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
- Mathematik | Informatik EDV | Informatik Informatik
Weitere Infos & Material
1. Introduction & Foundations.- 1. Various types of braids.- 2. A definition of a braid.- 3. An elementary move and braid equivalence.- 4. Braid projection.- 5. Braid permutation, pure braid.- 2. The Braid Group.- 1. Defunition of the braid group.- 2. A presentation for the braid group.- 3. The completeness of the relations.- 4. Elementary properties of the braid group.- 5. A braid invariant.- 3. Word Problem.- 1. Word problem for the braid group.- 2. A solution of the word problem.- 3. A presentation for the pure n-braid group.- 4. Special types of braids.- 1. Mexicar plaits.- 2. Generators of the Mexican plaits.- 3. An algorithm for Mexican plaits.- 4. Examples of the use of the algorithm.- 5. Quotient groups of the braid group.- 1. Sywumetric group and the braid group.- 2. Platoric solids and quotient groups of Bn.- 3. Finite quotient groups of B3.- 4. The firite quotient group B4(3).- 5. The finite quotient group B5(3).- 6. Isotopy of braids.- 1. Equivalence and isotopy.- 2. Words.- 3. Several interpretations of equivalence.- 4. Milnor invariant.- 7. Homotopy braid theory.- 1. Homotopy.- 2. Tangles and homotopy.- 3. Homotopy braid group.- 4. Homotopy braid invariants.- 5. Tangles and braids.- 8. Grom knots to braids.- 1. Knot theory — a quick review.- 2. Quasi-braids.- 3. Braided links.- 4. Alexander’s theorem.- 5. Knot invariants via braid invariants.- 9. Markov’s theorem.- 1. A theorem due to Markov.- 2. Proof of Markov’s theorem — I.- 3. Proof of Markov’s theorem — II.- 4. Applications.- 10. Knot invariants.- 1. Burau representation.- 2. Alexander polynomial.- 3. Jones polynomial.- 4. Alexander versus Jones.- 11. Braid groups on surfaces.- 1. Divac’s Problem.- 2. Braid group on S2.- 3. Braid group on the surface F.- 4. Braid group on P2.- 5. Braidgroup on T2.- 6. Word problem for Bn(S2).- 12. Algebraic equations.- 1. Configuration spaces.- 2. Complete solvability.- Appendix I — Group theory.- 1. Equivalence relation.- 2. Groups and a bit of ring theory.- 3. Free group.- 4. Presentations of groups.- 5. Word problem.- 6. Reidemeister-Schreier method, presentation of a subgroup.- 7. Triangle groups.- Appendix II — Topology.- 1. Fundamental concepts of Topology.- 2. Homotopy.- 3. Fundamental group.- 4. Manifolds.- Appendix III — Symplectic group.- 1. Symplectic group.- Appendix IV.- Appendix V.