Narrow Results

The first aim of this paper is to give an example of a virtual knot which vanishes all the known invariants and to show that it is a non-classical (in particular, non-trivial) knot. The second is to study some properties of the Z-polynomial of a virtual knot with virtual crossing number one and to show that there are infinitely many virtual knots with virtual crossing number two.

The depth of a link measures the minimum height of a resolving tree for the link whose leaves are all unlinks. We show that the depth of the closure of a strictly positive braid word is the length of the word minus the number of distinct letters.