In 1970 John Conway created a notion of a "tangle". Tangles can be seen as a building blocks of knots and are a basis of knot tabulation. Using tangles Conway managed to tabulate all knots up to 11 crossings, and links up to 10 crossings. Moreover, he found a bijection relation between rational numbers and a subclass of tangles called "rational tangles", thus fully classifying this subset of algebraic tangles.
Over 50 years later we extended Conway work. We introduced a binary tree notation, which helped us to define a unique "canonical representation" for algebraic tangles. This let us classify algebraic tangles up to 14 crossings. Moreover we studied symmetry groups of algebraic tangles.
During the talk I'll introduce you to the theory of tangles and present our results.
