可定向闭曲面I-丛一类自平环和中的本质曲面

Essential Closed Surfaces in a Class of the Self-annular Sum of I-bundles of Closed Surface

设M=S×I/A_0~A_1,其中S是可定向闭曲面,A_0,A_1落在S×{0}上,且A_0,A_1在S×I上均不可压缩.若A_0与A_1在S×{0}上都是非分离的平环,则M中不存在任何本质闭曲面.

Let M =S×I/A_0 ~A_1,where Sis an orientable closed surface,A_0,A_1 lie in S×{0}and are incompressible surfaces in S×I.If A_0 and A_1 are non-separating annular in S×{0},then there is no essential closed surface in M.