Positions and surfaces of a knot

(1)在与Kazuto Takao的联合工作中，我们发现存在一个3桥结，4桥不稳定的桥位置。(2)在与Atsushi石井和Kengo Kishimoto的一项联合工作中，对于一个外部是边界不可约的三体结，存在唯一的一组2-分解球，它们将局部1-句柄分解为合痕和环移动。在与Mario Eudave-Munoz的联合工作中，我们描述了1号隧道的2个类属-结。在与Yuya Koda的合作工作中，我们给出了一个分类的本质盘，annuli和tori在外部的一个属2 body-knot。(3)我们证明了均匀扭曲的纽结满足纽氏猜想。

(1) In a joint work with Kazuto Takao, we showed that there exists a 3-bridge knot with 4-bridge destabilized bridge position.(2) In a joint work with Atsushi Ishii and Kengo Kishimoto, for a handlebody-knot whose exterior is boundary-irreducible, there exists a unique set of 2-decomposing spheres which decompose local 1-handles up to isotopy and annulus-moves. In a joint work with Mario Eudave-Munoz, we characterized tunnel number 1 genus 2 handlebody-knots. In a joint work with Yuya Koda, we gave a classification of essential disks, annuli and tori in the exterior of a genus 2 handlebody-knot.(3) We showed that uniformly twisted knots satisfy the Neuwirth conjecture.