三维流形Heegaard分解的同调相交核

摘要

Let M be a closed connected oriented 3-manifold,(M;U,V;S)a Heegaard splitting for M.The main result of the present paper is as follows:Suppose the inclusions i:S→U,j:S→V induce the homomorphisms i#:H1(S)→H1(U),j#H1(S)→H1(V),then H2(M)=keri#∩kerj#.%本文主要考虑三维流形Heegaard分解的同调相交核,得到的主要结果如下：设（M;U,V;S）为3-流形M的Heegaard分解,包含映射i：S→U,J：S→V诱导的同调群同态分别为i#：H1（S）→H1（U）,j#：H1（s）→H1（V）,则H2（M）=keri#∩kerj#.