CF-MOVES FOR VIRTUAL LINKS

Oikawa defined an unknotting operation for virtual knots called a CF-move, and gave a classification of 2-component virtual links up to CF-moves by the virtual linking number and his n-invariant. In particular, it was proved that a CF-move characterizes the virtual linking numbers for 2-component odd virtual links. In this paper, we extend this result by clas-sifying odd virtual links and almost odd virtual links with arbitrary number of components up to CF-moves, using virtual linking numbers. Moreover, we extend Oikawa's n-invariant and introduce two invariants for 3-component even virtual links. Using these invariants together with virtual linking num-b ers, we classify 3-component even virtual links up to CF-moves. As a result, a classification of 3-component virtual links up to CF-moves is provided.