In the present paper, we investigate the non-Heegaard 2-compressible surfaces in small 3-manifolds, and show that such surfaces have some good properties.
In this paper, we fix the genus of SD-splittings of a compression body. We also discuss the uniqueness for minimal D-splittings and SD-splittings for a han-dlebody.
In the present paper, we characterize the bordered 3-manifolds with genus 1 D-splittingsand SD-splittings. We also describe a minimal genus SD-splitting for a handlebody and surface×I.
C lasp-pass移动是Habiro1993年在定向链环上引入的一个局部移动的概念.研究了几乎相邻的图,得到以下结论:对于一个几乎相邻图G,若它不包含价为1的顶点,则G的空间嵌入上的任意clasp-pass移动都可通过Δ-同伦来实现.作为推论,有:设f,g:G→S3是价为3的几乎相邻图G的两个顶点同伦的嵌入,若对于任意(1;3)阶有限型A3-等价不变量φ,φ(f)=φ(g),则f和g一定是de lta顶点同伦的.
