On a theorem on partially summing tangles by Lickorish

Abstract

Kirby and Lickorish have introduced the idea of prime tangle (5) where the term ‘tangle’ is borrowed from Conway (3). While exploring this notion, Lickorish has shown in ((6), theorem 3): A tangle, which is the Conway sum of two tangles, one of which is prime and connected to both arcs of the other one which itself is prime or untangle, is prime.