Franklin

An Invitation to Knot Theory : Virtual and Classical.

Author/Creator:
Dye, Heather A.
Publication:
Portland : CRC Press LLC, 2016.
Format/Description:
Book
1 online resource (287 pages)
Edition:
1st ed.
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Subjects:
Knot theory.
Form/Genre:
Electronic books.
Contents:
Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
List of Figures
List of Tables
Preface
Acknowledgments
About the author
Symbol List
SECTION I: Knots and crossings
CHAPTER 1: Virtual knots and links
1.1 CURVES IN THE PLANE
1.2 VIRTUAL LINKS
1.3 ORIENTED VIRTUAL LINK DIAGRAMS
1.4 OPEN PROBLEMS AND PROJECTS
CHAPTER 2: Linking invariants
2.1 CONDITIONAL STATEMENTS
2.2 WRITHE AND LINKING NUMBER
2.3 DIFFERENCE NUMBER
2.4 CROSSING WEIGHT NUMBERS
2.5 OPEN PROBLEMS AND PROJECTS
CHAPTER 3: A multiverse of knots
3.1 FLAT AND FREE LINKS
3.2 WELDED, SINGULAR, AND PSEUDO KNOTS
3.3 NEW KNOT THEORIES
3.4 OPEN PROBLEMS AND PROJECTS
CHAPTER 4: Crossing invariants
4.1 CROSSING NUMBERS
4.2 UNKNOTTING NUMBERS
4.3 UNKNOTTING SEQUENCE NUMBERS
4.4 OPEN PROBLEMS AND PROJECTS
CHAPTER 5: Constructing knots
5.1 SYMMETRY
5.2 TANGLES, MUTATION, AND PERIODIC LINKS
5.3 PERIODIC LINKS AND SATELLITE KNOTS
5.4 OPEN PROBLEMS AND PROJECTS
SECTION II: Knot polynomials
CHAPTER 6: The bracket polynomial
6.1 THE NORMALIZED KAUFFMAN BRACKET POLYNOMIAL
6.2 THE STATE SUM
6.3 THE IMAGE OF THE f-POLYNOMIAL
6.4 OPEN PROBLEMS AND PROJECTS
CHAPTER 7: Surfaces
7.1 SURFACES
7.2 CONSTRUCTIONS OF VIRTUAL LINKS
7.3 GENUS OF A VIRTUAL LINK
7.4 OPEN PROBLEMS AND PROJECTS
CHAPTER 8: Bracket polynomial II
8.1 STATES AND THE BOUNDARY PROPERTY
8.2 PROPER STATES
8.3 DIAGRAMS WITH ONE VIRTUAL CROSSING
8.4 OPEN PROBLEMS AND PROJECTS
CHAPTER 9: The checkerboard framing
9.1 CHECKERBOARD FRAMINGS
9.2 CUT POINTS
9.3 EXTENDING THE THEOREM
9.4 OPEN PROBLEMS AND PROJECTS
CHAPTER 10: Modifications of the bracket polynomial
10.1 THE FLAT BRACKET
10.2 THE ARROW POLYNOMIAL
10.3 VASSILIEV INVARIANTS.
10.4 OPEN PROBLEMS AND PROJECTS
SECTION III: Algebraic structures
CHAPTER 11: Quandles
11.1 TRICOLORING
11.2 QUANDLES
11.3 KNOT QUANDLES
11.4 OPEN PROBLEMS AND PROJECTS
CHAPTER 12: Knots and quandles
12.1 A LITTLE LINEAR ALGEBRA AND THE TREFOIL
12.2 THE DETERMINANT OF A KNOT
12.3 THE ALEXANDER POLYNOMIAL
12.4 THE FUNDAMENTAL GROUP
12.5 OPEN PROBLEMS AND PROJECTS
CHAPTER 13: Biquandles
13.1 THE BIQUANDLE STRUCTURE
13.2 THE GENERALIZED ALEXANDER POLYNOMIAL
13.3 OPEN PROBLEMS AND PROJECTS
CHAPTER 14: Gauss diagrams
14.1 GAUSS WORDS AND DIAGRAMS
14.2 PARITY AND PARITY INVARIANTS
14.3 CROSSING WEIGHT NUMBER
14.4 OPEN PROBLEMS AND PROJECTS
CHAPTER 15: Applications
15.1 QUANTUM COMPUTATION
15.2 TEXTILES
15.3 OPEN PROBLEMS AND PROJECTS
APPENDIX A: Tables
A.1 KNOT TABLES
A.2 KNOT INVARIANTS
APPENDIX B: References by chapter
B.1 CHAPTER 1
B.2 CHAPTER 2
B.3 CHAPTER 3
B.4 CHAPTER 4
B.5 CHAPTER 5
B.6 CHAPTER 6
B.7 CHAPTER 7
B.8 CHAPTER 8
B.9 CHAPTER 9
B.10 CHAPTER 10
B.11 CHAPTER 11
B.12 CHAPTER 12
B.13 CHAPTER 13
B.14 CHAPTER 14
B.15 CHAPTER 15
Index.
Notes:
Description based on publisher supplied metadata and other sources.
Local notes:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2021. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Other format:
Print version: Dye, Heather A. An Invitation to Knot Theory
ISBN:
9781498798617
9781498701648
OCLC:
958800440