Lectures in Knot Theory (Record no. 58346)
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| fixed length control field | 05365nam a22005895i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-031-40044-5 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20251030111722.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240315s2024 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783031400445 |
| -- | 978-3-031-40044-5 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-031-40044-5 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA613-613.8 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBP |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT038000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBP |
| Source | thema |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Przytycki, Józef H. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 73089 |
| 245 10 - TITLE STATEMENT | |
| Title | Lectures in Knot Theory |
| Medium | [electronic resource] : |
| Remainder of title | An Exploration of Contemporary Topics / |
| Statement of responsibility, etc. | by Józef H. Przytycki, Rhea Palak Bakshi, Dionne Ibarra, Gabriel Montoya-Vega, Deborah Weeks. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. 2024. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Cham : |
| Name of producer, publisher, distributor, manufacturer | Springer International Publishing : |
| -- | Imprint: Springer, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2024. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | XV, 520 p. 251 illus., 82 illus. in color. |
| Other physical details | online resource. |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS | |
| File type | text file |
| Encoding format | |
| Source | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | Universitext, |
| International Standard Serial Number | 2191-6675 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1. History of Knot Theory From Ancient Times to Gauss and His Student Listing -- 2. History of Knot Theory From Gauss to Jones -- 3. FROM FOX 3-COLORING TO THE YANG-BAXTER OPERATOR -- 4. Lecture ?: Goeritz and Seifert Matrices -- 5. Chapter Heading -- 6. The HOMFLYPT and the 2-variable Kauffman Polynomial -- 7. Lecture 8: The Temperley - Lieb Algebra and Braid Groups -- 8. Lecture 9: Symmetrizers of Finite Groups and Jones-Wenzl Idempotents -- 9. Lecture 10: Plucking polynomial of rooted trees and its use in knot theory -- 10. Lecture 11: Basics of Skein Modules -- 11. Lecture 12: The Kauffman Bracket Skein Module -- 12. Lecture 13: The Kauffman Bracket Skein Module and Algebra of Surface I-bundles -- 13. Lecture 14: Multiplicative Structure of the Kauffman Bracket Skein Algebra of the Thickened T-Shirt -- 14. Spin Structure and the Framing Skein Module of Links in 3-Manifolds -- 15. Lecture 16: The Witten - Reshetikhin - Turaev Invariant of 3-manifolds -- 16. Lecture 19: Type A Gram determinant.-17. Lecture 18: Gram Determinants of Type B and Type M b -- 18. Lecture 19: Khovanov homology: a categorification of The Jones polynomial -- 19. Lecture 20: Long Exact Sequence of Khovanov Homology and Torsion -- 20. Lecture 21: Categorification of Skein Modules of Twisted I-bundles over surfaces -- Appendix A: Basics of 3-Dimensional Topology. -Appendix B: Surgery on Links in the 3-Sphere and Kirby's Calculus. -Glossary -- SOlutions. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | This text is based on lectures delivered by the first author on various, often nonstandard, parts of knot theory and related subjects. By exploring contemporary topics in knot theory including those that have become mainstream, such as skein modules, Khovanov homology and Gram determinants motivated by knots, this book offers an innovative extension to the existing literature. Each lecture begins with a historical overview of a topic and gives motivation for the development of that subject. Understanding of most of the material in the book requires only a basic knowledge of topology and abstract algebra. The intended audience is beginning and advanced graduate students, advanced undergraduate students, and researchers interested in knot theory and its relations with other disciplines within mathematics, physics, biology, and chemistry. Inclusion of many exercises, open problems, and conjectures enables the reader to enhance their understanding of the subject. The use of this text for the classroom is versatile and depends on the course level and choices made by the instructor. Suggestions for variations in course coverage are included in the Preface. The lecture style and array of topical coverage are hoped to inspire independent research and applications of the methods described in the book to other disciplines of science. An introduction to the topology of 3-dimensional manifolds is included in Appendices A and B. Lastly, Appendix C includes a Table of Knots. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 69683 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 72027 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 72028 |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 73090 |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 72029 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Bakshi, Rhea Palak. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 73091 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Ibarra, Dionne. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 73092 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Montoya-Vega, Gabriel. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 73093 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Weeks, Deborah. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 73094 |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer Nature eBook |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031400438 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031400452 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Universitext, |
| International Standard Serial Number | 2191-6675 |
| 9 (RLIN) | 73095 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1007/978-3-031-40044-5">https://doi.org/10.1007/978-3-031-40044-5</a> |
| 912 ## - | |
| -- | ZDB-2-SMA |
| 912 ## - | |
| -- | ZDB-2-SXMS |
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