An Introduction to Knot Theory

This paper concentrates on the construction of invariants of knots, such as the Jones polynomials and the Vassiliev invariants, and the relationships of these invariants to other mathematics (such as Lie algebras).

[1]  J. W. Alexander Topological invariants of knots and links , 1928 .

[2]  J. Conway An enumeration of knots and links, and some of their algebraic properties , 1970 .

[3]  Louis H. Kauffman The conway polynomial , 1981 .

[4]  David Joyce,et al.  A classifying invariant of knots, the knot quandle , 1982 .

[5]  Louis H. Kauffman,et al.  Formal Knot Theory , 1983 .

[6]  Vaughan F. R. Jones Index for subfactors , 1983 .

[7]  Kenneth C. Millett,et al.  A new polynomial invariant of knots and links , 1985 .

[8]  V. Jones A polynomial invariant for knots via von Neumann algebras , 1985 .

[9]  Louis H. Kauffman,et al.  State Models and the Jones Polynomial , 1987 .

[10]  Knot Invariants and the Critical Statistical Systems , 1987 .

[11]  Kunio Murasugi Jones polynomials and classical conjectures in knot theory , 1987 .

[12]  Vaughan F. R. Jones,et al.  Hecke algebra representations of braid groups and link polynomials , 1987 .

[13]  Jozef H. Przytycki,et al.  Invariants of links of Conway type , 1988, 1610.06679.

[14]  Vaughan F. R. Jones,et al.  On knot invariants related to some statistical mechanical models , 1989 .

[15]  Victor A. Vassiliev,et al.  Cohomology of knot spaces , 1990 .

[16]  Louis H. Kauffman,et al.  An invariant of regular isotopy , 1990 .

[17]  L. Kauffman Knots And Physics , 1991 .

[18]  Roger Fenn,et al.  RACKS AND LINKS IN CODIMENSION TWO , 1992 .

[19]  M. Thistlethwaite,et al.  The classification of alternating links , 1993 .

[20]  J. Birman,et al.  Knot polynomials and Vassiliev's invariants , 1993 .

[21]  Dror Bar-Natan,et al.  On the Vassiliev knot invariants , 1995 .

[22]  T. Stanford Finite-type invariants of knots, links, and graphs , 1996 .

[23]  Frank Harary,et al.  Knots and Graphs I-Arc Graphs and Colorings , 1999 .