The Layered Surface And The Cases Of Crossing Splittings Of A Kind Of Knot

Twist knot is an important branch of knot theory, which has many special properties. Layered surface for knots is a new kind of spanning surface and this surface is the generalization of Seifert surface. In this article, performing the Minimal Genus Algorithm on Twist knot J(2, n) and Pretzel knot, we can get the Layered surfaces with the minimal genus. And we show that the Layered surfaces with the minimal genus are impressing and basic Layered surfaces.In this article, we also analyze the crossing splittings of T2 which is a part of J(2, n) and get the results. Besides, we show that the results of crossing splittings are not concerned with the positions of these crossings in T2.