ABSTRACT
Long virtual knots and their invariants first appeared in [GPV]. The present chapter consists of the author’s results. The two main arguments that can be taken into account in the theory of “long” virtual knots and could not be used before, are the following:
1. One can indicate the initial and the final arcs (which are not compact) of the quandle; the elements corresponding to them are invariant under generalised Reidemeister moves.
