3-流形沿不可压缩曲面的融合(amalgamation)及性质

The amalgamation of 3-manifolds along incompressible surface and its property

主要研究了3-流形融合的一些性质,特别是两个3-流形沿不可压缩曲面融合的情形.设FiMi为3-流形Mi中的不可压缩曲面,h:F1→F2为一同胚,M=M1∪hM2.给出了不可压缩曲面Fi满足一定的条件时,两个3-流形M1和M2的融合M有不可压缩的边界.讨论了在两个3-流形M1和M2都不可约的基础上,M也是不可约的.由上述的两个结果,得到了一些相应的推论.

Some properties of amalgamation of 3-manifolds are mainly discussed. Particularly, we deal with the case in which two manifolds are amalgamated along incompressible surface. Let Fi belong to δMi be an incompressible surface in 3-manifold Mi,h：F1→F2 a homeomorphism, M = M1 ∪hM2. The amalgamation M of two 3-manifolds M1 and M2 with incompressible boundary is given when incompressible surface Fi satisfies certain conditions. On the basis of the irreduciblities of two 3-manifolds M1 and M2, we discuss that the amalgamation M of them is irreducible. We also obtain some corresponding corollaries for the above two results.