带边Seifert流形的H′-分解的结构

The structures of the H′-splittings of Seifert manifold with boundary

已知任意紧致连通可定向三维流形M都有H′-分解,即存在M中一个紧致连通可定向曲面F,F把M切成两个柄体H1和H2,H1∩H2=F,H1∪FH2=M.显见,当M是闭三维流形时,H′-分解与经典Heegaard分解是一致的;当M是带边三维流形时,H′-分解与Heegaard分解是不同的分解.研究了紧致连通可定向带边Seifert流形的H′-分解的结构,主要结果给出这类流形的H′-分解的特征描述.

It is known that each compact connected orientable 3-manifold M admits a H′-splitting.That is,there is a compact connected orientable surface F in M,and F splits M into two handlebodies H1 and H2,satisfying H1∩H2=F and H1∪F H2=M.Obviously,when M is a closed 3-manifold,H′-splitting is consistent with classical Heegaard splitting.When M is a 3-manifold with boundary,H′-splitting and Heegaard splitting are different.In this paper,the structures of the H′-splittings of the compact connected orientable Seifert manifold with boundary are studied.The characteristics of H′-splittings of this kind of manifold are given in main results.