On the Homotopy Types of the Groups of Equivariant Diffeomorphisms
On the Homotopy Types of the Groups of Equivariant Diffeomorphisms
复制标题
等变微分同胚群的同伦类型
DOI：
10.2977/prims/1195187218
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发表时间：
1980
期刊：
影响因子：
--
通讯作者：
K. Abe
中科院分区：
文献类型：
--
作者：
K. Abe
本文的目的是研究当 G 是紧李群且轨道空间 M/G 同胚于单位区间 [0, 1] 时，闭连通光滑 G 流形 M 的等变微分同胚群的同伦型。令 Diffg (M)0 表示 G 流形 M 的等变 C°° 微分同胚群，其是恒等式的 G 同位素，具有 C°° 拓扑。如果M/G同胚于[0, 1]，则M有两种或三种轨道类型G/H、G/K0和GjKl。我们可以选择满足HdK0nK1的各向同性子群H、K0、K^。此外，M 的 G 流形结构由因子组 N(H)/H9 的元素 r1 确定，其中 N(H) 是 G 中 H 的归一化器（参见§1）。令 Q(N(H)/H; (N(H) fl N(K0))IH, (N(H) n N(rjK1ri~ y)IH)0 表示路径 a 的空间恒等式的连通分量： [0, l]-+N(H)IH 满足 a(0)e(N(H) n N(X0))/H 和 a(l)e(N(H) n
The purpose of this paper is to study the homotopy type of the group of the equivariant diffeomorphisms of a closed connected smooth G-manifold M, when G is a compact Lie group and the orbit space M/G is homeomorphic to a unit interval [0, 1]. Let Diffg (M)0 denote the group of equivariant C°° diffeomorphisms of the G-manifold M which are G-isotopic to the identity, endowed with C°° topology. If M/G is homeomorphic to [0, 1], then M has two or three orbit types G/H, G/K0 and GjKl. We can choose the isotropy subgroups H, K0, K^ satisfying HdK0nK1. Moreover the G-manifold structure of M is determined by an element r\ of a factor group N(H)/H9 where N(H) is the normalizer of H in G (see §1). Let Q(N(H)/H; (N(H) fl N(K0))IH, (N(H) n N(rjK1ri~ y)IH)0 denote the connected component of the identity of the space of paths a: [0, l]-+N(H)IH satisfying a(0)e(N(H) n N(X0))/H and a(l)e(N(H) n