三维流形Heegaard分解的同调分解同态

摘要

Let M be a closed connected oriented 3 - manifold, U∪ s V a Heegaard splitting for M. The splitting homo-morphism of a Heegaard splitting with respect to the first homology group of M is considered. The inclusions i:S→U, j:S→V induce the homomorphisms i#:H1 (S)→H1 (U), j#: H1 (S)→H1 (V). The homological splitting homomor-phism(i#, j#) :H1 (S) →H1 (U) ×H1(V) of U∪sV is studied. Some properties of (i#, j#) are given.%考虑Heegaard分解U∪sV的同调分解同态,包含映射i:S→U,j:S→V诱导了同调群同态i#:H1(S)→H1(U),j#:H1(S)→H1(V).研究可定向闭三维流形M的Heegaard分解U∪sV的同调分解同态(i#,j#):H1(S)→H1(U)×H1(V),得到同调分解同态的若干性质.