非平凡压缩体中的本质非扩展平环极大组

设A是真嵌入于亏格为2的柄体中的极大本质平环组,一个已知的结果是1≤|A|≤3.将以上结果推广得到:若A是真嵌入于亏格为g(≥3)的柄体中的极大本质平环组,则2≤|A|≤4g-5,且2和4g-5分别是上下确界.进一步推广以上结论,证明了一个非平凡压缩体C中的一个非扩展极大本质平环组至多包含4h-b个平环,且4h-b是上确界,其中h表示从曲面(δ)_C×1得到C所需粘的1-柄的个数,b表示C的副边界分支的个数.

Maximal collections of non-spanning essential annuli in a non-trivial compression body

It is known that for a maximal collection A of pairwise disjoint non-parallel essential annuli in a handlebody of genus 2, 1≤|A|≤3. It is generalized the result that for a maximal collection of pairwise disjoint non-parallel essential annuli in a handlebody of genus g(≥3 ), 2≤|A|≤4g -5,and the bounds are sharp. It is shown that for a maximal collection A of pairwise disjoint non-parallel essential non-spanning annuli in a nontrivial compression body C,|A|≤4h - b, where h is the total number of 1-handles attached to obtain C, and b is the number of components of (δ)_ C, and the bound is sharp.