Classical roots of knot theory

Classical Knot Theory

This paper is a very brief introduction to knot theory. It describes knot coloring by quandles, the fundamental group of a knot complement, and handle-decompositions of knot complements.

Jones Polynomials and Classical Conjectures in Knot Theory

The primeness is necessary in the last statement ofTheorem B, since the connected sum of two figure eight knots is alternating, but it has a minimal non-alternating projection. Note that the figure eight knot is amphicheiral. Theorems A and B follow easily from Theorems l-4 (stated below) which show strong connections between c(L) and the Jones polynomial Vr(t). Let d maxVL(t) and d,i,v~(t) den...

Computation of hyperbolic structures in knot theory THIN POSITION IN THE THEORY OF CLASSICAL KNOTS

This is a preliminary version of a chapter that is intended to appear in the “Handbook of Knot Theory”, edited by William W. Menasco and Morwen B. Thistlethwaite. Comments are welcome. For our purposes, “knot theory” will have the narrowest interpretation: the study of isotopy classes of locally flat embeddings of the circle S in S. The distinctions between smooth, PL, and locally flat topologi...

Knot Theory

Banff Workshop Proposal: Knot Theory and Virtual Knot Theory

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