A lower bound of the crossing number of composite knots (2407.10467v1)

Abstract: Let $c(K)$ denote the crossing number of a knot $K$ and let $K_1# K_2$ denote the connected sum of two oriented knots $K_1$ and $K_2$. It is a very old unsolved question that whether $c(K_1# K_2)=c(K_1)+c(K_2)$. In this paper we show that $c(K_1# K_2)> (c(K_1)+c(K_2))/16$.