Ayaka Shimizu (NIT, Gunma College, Japan)
The reductivity of a knot projection is defined to be the minimum number of splices required to make the projection reducible, where the splices are applied to a knot projection resulting in another knot projection. It has been shown that the reductivity is four or less for any knot projection and shown that there are infinitely many knot projections with reductivity 0, 1, 2, and 3. The “reductivity problem” is a problem asking the existence of a knot projection whose reductivity is four. In this talk, we will discuss some strategies for the reductivity problem focusing on the region of a knot projection.