Isotopy classes of diffeomorphisms of (k-1)-connected almost-parallelizable 2k-manifolds
Isotopy classes of diffeomorphisms of (k-1)-connected almost-parallelizable 2k-manifolds
复制标题
(k-1) 连接的几乎可并行的 2k 流形的微分同象的同位素类
DOI：
10.1007/bfb0088108
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发表时间：
1979
影响因子：
3.1
通讯作者：
M. Kreck
中科院分区：
文献类型：
--
作者：
M. Kreck
§ 1 结果封闭定向可微流形 M 上保定向微分同胚的同位素类群用 iToDiff (M) 表示；伪同位素类别组用~roDlff (M) 表示。在本文中，我们将根据 k~ 3 的精确序列计算 M 的~ oDiff (M)，一个闭可微 (k-1) 连接的几乎可并行 2k 流形，并对任何简单连接的闭可微 4-流形的 ~ oDiff (M) 中的元素进行分类。在下文中，M 代表一个闭可微 (k-1) 连接的几乎可并行 2k 流形，如果 k) 3如果 k= 2，则为单连通流形。为了描述我们的结果，我们需要一些不变量。我们用 Aut Hk (M) 表示 Hk (M):= Hk (M; Z) 的自同构群，保留 M 上的交集形式，并且（对于 k~ 3）与函数~: Hk (M)>~ k_l (SO (k)) 交换，它将表示 x 的嵌入球体的法向丛的分类图分配给 X~ Hk (M)。由于任何方向保持微分同态的同源诱导图位于 Aut Hk (M) 中，因此我们得到同态
§ 1 ResultsThe group of isotopy classes of orientation preserving diffeomorphisms on a closed oriented differentiable manifold M is denoted by iToDiff (M); the group of pseudo isotopy classes is denoted by~ roDlff (M). In this paper we will compute~ oDiff (M) for M a closed differentiable (k-1)-connected almost-paralleli zable 2k-manifold in terms of exact sequences for k~ 3, and classify elements in~ oDiff (M) for any simply-connected closed differentiable 4-manifold.In the following M stands for a closed differentiable (k-1)-connected almostparallelizable 2k-manifold if k) 3 and a simply-connected manifold if k= 2. To describe our results we need some invariants. We denote by Aut Hk (M) the group of automorphisms of Hk (M):= Hk (M; Z) preserving the intersection form on M and (for k~ 3) commuting with the function~: Hk (M)>~ k_l (SO (k)), which assigns to X~ Hk (M) the classifying map of the normal bundle of an embedded sphere representing x. As the induced map in homology of any orientation preserving diffeomorphism lies in Aut Hk (M), we obtain a homomorphism