ON CROSSING NUMBER OF KNOTS

Abstract

The aim of this paper is to endow a monoid structure (cid:85) on the set S of all oriented knots(links) under the operation , called addition of knots. Moreover, we prove that there exists a homomorphism of monoids between (Sd, ) to (N, +), where Sd is a subset of S with an extra condition and N is the monoid of non negative integers under usual addition.

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