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In Chapter 6, we describe the concept of braid equivalence from the topological point of view. This will lead us to a new concept braid homotopy that is discussed fully in the next chapte… Altro …

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[EAN: 9789048152452], Neubuch, [SC: 0.0], [PU: Springer Netherlands], GROUPTHEORY; HOMOTOPY; MATHEMATICA; ALGEBRA; MATHEMATICS, Druck auf Anfrage Neuware -In Chapter 6, we describe the co… Altro …

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A Study of Braids (Mathematics and Its Applications, 484, Band 484) - edizione con copertina flessibile

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ISBN: 9789048152452

Mitwirkende: Kurpita, Bohdan I. Springer Netherlands, Taschenbuch, Auflage: Softcover reprint of hardcover 1st ed. 1999, 288 Seiten, Publiziert: 2009-12-28T00:00:01Z, Produktgruppe: Buch,… Altro …

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A Study of Braids (Mathematics and Its Applications, 484, Band 484) - edizione con copertina flessibile

2009, ISBN: 9789048152452

Mitwirkende: Kurpita, Bohdan I. Springer Netherlands, Taschenbuch, Auflage: Softcover reprint of hardcover 1st ed. 1999, 288 Seiten, Publiziert: 2009-12-28T00:00:01Z, Produktgruppe: Buch,… Altro …

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A Study of Braids (Mathematics and Its Applications, 484, Band 484) - edizione con copertina flessibile

2009, ISBN: 9789048152452

Mitwirkende: Kurpita, Bohdan I. Springer Netherlands, Taschenbuch, Auflage: Softcover reprint of hardcover 1st ed. 1999, 288 Seiten, Publiziert: 2009-12-28T00:00:01Z, Produktgruppe: Buch,… Altro …

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A Study of Braids (Mathematics and Its Applications, 484, Band 484)
Autore:
Titolo:
ISBN:

9789048152452


This book provides a comprehensive exposition of the theory of braids, beginning with the basic mathematical definitions and structures. Among the many topics explained in detail are: the braid group for various surfaces; the solution of the word problem for the braid group; braids in the context of knots and links (Alexander's theorem); Markov's theorem and its use in obtaining braid invariants; the connection between the Platonic solids (regular polyhedra) and braids; the use of braids in the solution of algebraic equations. Dirac's problem and special types of braids termed Mexican plaits are also discussed. Audience: Since the book relies on concepts and techniques from algebra and topology, the authors also provide a couple of appendices that cover the necessary material from these two branches of mathematics. Hence, the book is accessible not only to mathematicians but also to anybody who might have an interest in the theory of braids. In particular, as more and more applications of braid theory are found outside the realm of mathematics, this book is ideal for any physicist, chemist or biologist who would like to understand the mathematics of braids. With its use of numerous figures to explain clearly the mathematics, and exercises to solidify the understanding, this book may also be used as a textbook for a course on knots and braids, or as a supplementary textbook for a course on topology or algebra.

Informazioni dettagliate del libro - A Study of Braids (Mathematics and Its Applications, 484, Band 484)


EAN (ISBN-13): 9789048152452
ISBN (ISBN-10): 9048152453
Copertina rigida
Copertina flessibile
Anno di pubblicazione: 2010
Editore: Springer Netherlands
288 Pagine
Peso: 0,439 kg
Lingua: eng/Englisch

Libro nella banca dati dal 2012-07-02T04:58:52+02:00 (Rome)
Pagina di dettaglio ultima modifica in 2024-01-31T11:29:31+01:00 (Rome)
ISBN/EAN: 9789048152452

ISBN - Stili di scrittura alternativi:
90-481-5245-3, 978-90-481-5245-2
Stili di scrittura alternativi e concetti di ricerca simili:
Autore del libro : kunio, study braids

Dati dell'editore

Autore: Kunio Murasugi; B. Kurpita
Titolo: Mathematics and Its Applications; A Study of Braids
Editore: Springer; Springer Netherland
277 Pagine
Anno di pubblicazione: 2010-12-15
Dordrecht; NL
Stampato / Fatto in
Lingua: Inglese
53,49 € (DE)
54,99 € (AT)
59,00 CHF (CH)
POD
X, 277 p.

BC; Hardcover, Softcover / Mathematik/Geometrie; Algebraische Topologie; Verstehen; Group theory; Homotopy; Mathematica; algebra; mathematics; Algebraic Topology; Group Theory and Generalizations; Manifolds and Cell Complexes; Geometry; Discrete Mathematics in Computer Science; Gruppen und Gruppentheorie; Topologie; Geometrie; Mathematik für Informatiker; Diskrete Mathematik; BB

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.

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