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An Invitation to Knot Theory: Virtual and Classical

Heather A. Dye
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2016
Number of Pages: 
256
Format: 
Hardcover
Price: 
59.95
ISBN: 
9781498701648
Category: 
Textbook
We do not plan to review this book.

Knots and crossings
Virtual knots and links
CURVES IN THE PLANE
VIRTUAL LINKS
ORIENTED VIRTUAL LINK DIAGRAMS

 

Linking invariants
CONDITIONAL STATEMENTS
WRITHE AND LINKING NUMBER
DIFFERENCE NUMBER
CROSSING WEIGHT NUMBERS

 

A multiverse of knots
FLAT AND FREE LINKS
WELDED, SINGULAR, AND PSEUDO KNOTS
NEW KNOT THEORIES

 

Crossing invariants
CROSSING NUMBERS
UNKNOTTING NUMBERS
UNKNOTTING SEQUENCE NUMBERS

 

Constructing knots
SYMMETRY
TANGLES, MUTATION, AND PERIODIC LINKS
PERIODIC LINKS AND SATELLITE KNOTS

 

Knot polynomials
The bracket polynomial

THE NORMALIZED KAUFFMAN BRACKET POLYNOMIAL
THE STATE SUM
THE IMAGE OF THE F-POLYNOMIAL

 

Surfaces
SURFACES
CONSTRUCTIONS OF VIRTUAL LINKS
GENUS OF A VIRTUAL LINK

 

Bracket polynomial II
STATES AND THE BOUNDARY PROPERTY
PROPER STATES
DIAGRAMS WITH ONE VIRTUAL CROSSING

 

The checkerboard framing
CHECKERBOARD FRAMINGS
CUT POINTS
EXTENDING THE KAUFFMAN-MURASUGI-THISTLETHWAITE THEOREM

 

Modifications of the bracket polynomial
THE FLAT BRACKET
THE ARROW POLYNOMIAL
VASSILIEV INVARIANTS

 

Algebraic structures
Quandles

TRICOLORING
QUANDLES
KNOT QUANDLES

 

Knots and quandles
A LITTLE LINEAR ALGEBRA AND THE TREFOIL
THE DETERMINANT OF A KNOT
THE ALEXANDER POLYNOMIAL
THE FUNDAMENTAL GROUP

 

Biquandles
THE BIQUANDLE STRUCTURE
THE GENERALIZED ALEXANDER POLYNOMIAL

 

Gauss diagrams
GAUSS WORDS AND DIAGRAMS
PARITY AND PARITY INVARIANTS
CROSSING WEIGHT NUMBER

 

Applications
QUANTUM COMPUTATION
TEXTILES

 

Appendix A: Tables
Appendix B: References by Chapter