The Resource A Study of Braids, by Kunio Murasugi, B. Kurpita, (electronic resource)

A Study of Braids, by Kunio Murasugi, B. Kurpita, (electronic resource)

Label
A Study of Braids
Title
A Study of Braids
Statement of responsibility
by Kunio Murasugi, B. Kurpita
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
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 chapter. As just mentioned, in Chapter 7, we shall discuss the difference between braid equivalence and braid homotopy. Also in this chapter, we define a homotopy braid invariant that turns out to be the so-called Milnor number. Chapter 8 is a quick review of knot theory, including Alexander's theorem. While, Chapters 9 is devoted to Markov's theorem, which allows the application of this theory to other fields. This was one of the motivations Artin had in mind when he began studying braid theory. In Chapter 10, we discuss the primary applications of braid theory to knot theory, including the introduction of the most important invariants of knot theory, the Alexander polynomial and the Jones polynomial. In Chapter 11, motivated by Dirac's string problem, the ordinary braid group is generalized to the braid groups of various surfaces. We discuss these groups from an intuitive and diagrammatic point of view. In the last short chapter 12, we present without proof one theorem, due to Gorin and Lin [GoL] , that is a surprising application of braid theory to the theory of algebraic equations
Member of
http://library.link/vocab/creatorName
Murasugi, Kunio
Dewey number
514.2
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • Zz4h_CPc5zY
  • YFTMskNylpQ
Image bit depth
0
Language note
English
LC call number
QA612-612.8
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Kurpita, B.
Series statement
Mathematics and Its Applications
Series volume
484
http://library.link/vocab/subjectName
  • Algebraic topology
  • Group theory
  • Cell aggregation
  • Geometry
  • Computational complexity
  • Algebraic Topology
  • Group Theory and Generalizations
  • Manifolds and Cell Complexes (incl. Diff.Topology)
  • Geometry
  • Discrete Mathematics in Computer Science
Label
A Study of Braids, by Kunio Murasugi, B. Kurpita, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
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. Braid group 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
Dimensions
unknown
Edition
1st ed. 1999.
Extent
1 online resource (X, 277 p.)
File format
multiple file formats
Form of item
online
Isbn
9789401593199
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-94-015-9319-9
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000124870
  • (SSID)ssj0001298646
  • (PQKBManifestationID)11751644
  • (PQKBTitleCode)TC0001298646
  • (PQKBWorkID)11242882
  • (PQKB)11687614
  • (DE-He213)978-94-015-9319-9
  • (MiAaPQ)EBC4712344
  • (EXLCZ)993400000000124870
Label
A Study of Braids, by Kunio Murasugi, B. Kurpita, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
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. Braid group 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
Dimensions
unknown
Edition
1st ed. 1999.
Extent
1 online resource (X, 277 p.)
File format
multiple file formats
Form of item
online
Isbn
9789401593199
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-94-015-9319-9
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000124870
  • (SSID)ssj0001298646
  • (PQKBManifestationID)11751644
  • (PQKBTitleCode)TC0001298646
  • (PQKBWorkID)11242882
  • (PQKB)11687614
  • (DE-He213)978-94-015-9319-9
  • (MiAaPQ)EBC4712344
  • (EXLCZ)993400000000124870

Library Locations

  • Architecture LibraryBorrow it
    Gould Hall 830 Van Vleet Oval Rm. 105, Norman, OK, 73019, US
    35.205706 -97.445050
  • Bizzell Memorial LibraryBorrow it
    401 W. Brooks St., Norman, OK, 73019, US
    35.207487 -97.447906
  • Boorstin CollectionBorrow it
    401 W. Brooks St., Norman, OK, 73019, US
    35.207487 -97.447906
  • Chinese Literature Translation ArchiveBorrow it
    401 W. Brooks St., RM 414, Norman, OK, 73019, US
    35.207487 -97.447906
  • Engineering LibraryBorrow it
    Felgar Hall 865 Asp Avenue, Rm. 222, Norman, OK, 73019, US
    35.205706 -97.445050
  • Fine Arts LibraryBorrow it
    Catlett Music Center 500 West Boyd Street, Rm. 20, Norman, OK, 73019, US
    35.210371 -97.448244
  • Harry W. Bass Business History CollectionBorrow it
    401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US
    35.207487 -97.447906
  • History of Science CollectionsBorrow it
    401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US
    35.207487 -97.447906
  • John and Mary Nichols Rare Books and Special CollectionsBorrow it
    401 W. Brooks St., Rm. 509NW, Norman, OK, 73019, US
    35.207487 -97.447906
  • Library Service CenterBorrow it
    2601 Technology Place, Norman, OK, 73019, US
    35.185561 -97.398361
  • Price College Digital LibraryBorrow it
    Adams Hall 102 307 West Brooks St., Norman, OK, 73019, US
    35.210371 -97.448244
  • Western History CollectionsBorrow it
    Monnet Hall 630 Parrington Oval, Rm. 300, Norman, OK, 73019, US
    35.209584 -97.445414
Processing Feedback ...