Additivity of Crossing Number via Restricted Reidemeister Moves

Abstract

We define a set of restricted Reidemeister moves and show that if $K$ is obtained from $K_0\#K_1$ using those moves, then the crossing number of $K$ is at least $c(K_0)+c(K_1)$. We also explore topological interpretations of this result.

45 pages, 13 figures