N-STRING TANGLES

Abstract

An n-string tangle (B, T) is a 3-ball B containing n properly embedded arcs T={ti}. An n-string tangle (B, T) is called rational if it is a homeo-morphism of pairs from (B, T) to (D, P)×I where D is the unit disk, P is any set of n points in the interior of D and I is the unit interval on the real line. In this article we begin to generalize the well known classification of 2-string rational tangles to rational tangles with three or more strings. A symbol describing an n-string rational tangle and an algebraic topological invariant is developed.