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

作　　者：李阳[1] 雷逢春[2] 

机构地区：[1]北京工商大学数理系,北京100037 [2]大连理工大学应用数学系,辽宁大连116024

出　　处：《辽宁师范大学学报（自然科学版）》2008年第3期267-269,共3页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(10571034)

摘　　要：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.

关 键 词：3-流形的融合 不可压缩曲面 不可约曲面 柄体 

分 类 号：O189.21[理学—数学]