大距离Heegaard分解的三穿孔球面和

The Pants Sum of High Distance Heegaard Splittings

中文关键词:  三穿孔球面和  Heegaard距离  Heegaard亏格.

英文关键词:pants sum  Heegaard distance  Heegaard genus.

中文摘要:

      设$M_i~(i=1,2)$是一个紧致可定向的三维流形, $F_i$是$M_i$边界上的一个不可压缩曲面, $M=M_{1}\cup_{f}M_{2}$, 其中$f$是$F_1$到$F_2$一个同胚,对于具有特定条件的相粘曲面$F_i$, 如果$M_i$具有一个Heegaard距离至少是$2(g(M_1)+g(M_2))+1$的Heegaard分解,则$g(M)=g(M_1)+g(M_2)$.

英文摘要:

      Let $M_i$ be a compact orientable 3-manifold, and $F_i$ be an incompressible surface on $\partial M_i$, $i=1,2$. Let $f: F_1\rightarrow F_2$ be a homeomorphism, and $M=M_{1}\cup_{f} M_{2}$. In this paper, under certain assumptions for the attaching surface $F_i$, we show that if both $M_1$ and $M_2$ have Heegaard splittings with distance at least $2(g(M_1)+g(M_2))+1$, then $g(M)=g(M_1)+g(M_2)$.