Singular fibers of stable maps of manifold pairs and their applications
Singular fibers of stable maps of manifold pairs and their applications
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流形对稳定映射的奇异纤维及其应用
DOI：
10.1007/978-3-319-73639-6_8
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
O. Saeki and T. Yamamoto
中科院分区：
文献类型：
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作者：
R.I. Baykur and O. Saeki;O. Saeki and T. Yamamoto
设（M，N）是一个流形对，其中M是一个闭三维流形，N是M的一个闭二维子流形.本文首先将（M，N）的稳定映射的奇异纤维分类为曲面。然后，我们计算了奇异纤维的泛复形的上同调群，得到了流形对上莫尔斯函数的某些协边不变量，其中是一个闭曲面，是的一个闭一维子流形。当子流形将周围流形分成两部分时，我们也给出了所有这些结果的2-着色版本。
Let (M,N) be a manifold pair, whereMis a closed 3-dimensional manifold andNis a closed 2-dimensional submanifold ofM. In this paper, we first classify singular fibers ofstable maps of (M,N) into surfaces. Then, we compute the cohomology groups of the associated universal complex of singular fibers, and obtain certain cobordism invariants for Morse functions on manifold pairs, whereis a closed surface andis a closed 1-dimensional submanifold of. We also give the 2-colored versions of all these results, when the submanifold separates the ambient manifold into two parts.