ON THE UNIFORM SIMPLICITY OF DIFFEOMORPHISM GROUPS
ON THE UNIFORM SIMPLICITY OF DIFFEOMORPHISM GROUPS
复制标题
DOI：
10.1142/9789814261173_0004
复制
发表时间：
2009-04
期刊：
影响因子：
--
通讯作者：
T. Tsuboi
中科院分区：
文献类型：
--
作者：
T. Tsuboi
本文证明了紧致连通n维流形Mn的Cr个同态群Diff（Mn）（1 ≤ r ≤ ∞，r = n+1）的单位分支Diff（M）0的一致单性，其中Mn具有不含中间指标n/2的柄分解.更精确地说，对于这样的Diff（M）0 \{id}的任何元素f和g，f可以写成g或g−1的至多16 n +28个共轭的乘积，我们用f ∈（Cg）表示。我们对几个流形有更好的估计。对于n维球面Sn，对Diff（S）0 \ {id}（1 ≤ r ≤ ∞，r = n + 1）的任意元素f和g，f ∈（Cg）;对于紧致连通3-流形M3，对Diff（M）0 \ {id}（1 ≤ r ≤ ∞，r = 4）的任意元素f和g，f ∈（Cg）. 1991年数学学科分类。初级57 R52、57 R50;次级37 C 05
We show the uniform simplicity of the identity component Diff(M)0 of the group of Cr diffeomorphisms Diff (Mn) (1 ≤ r ≤ ∞, r = n+1) of the compact connected n-dimensional manifold Mn with handle decomposition without handles of the middle index n/2. More precisely, for any elements f and g of such Diff(M)0 \{id}, f can be written as a product of at most 16n+28 conjugates of g or g−1, which we denote by f ∈ (Cg). We have better estimates for several manifolds. For the n-dimensional sphere Sn, for any elements f and g of Diff(S)0 \ {id} (1 ≤ r ≤ ∞, r = n + 1), f ∈ (Cg), and for a compact connected 3-manifold M3, for any elements f and g of Diff(M)0 \ {id} (1 ≤ r ≤ ∞, r = 4), f ∈ (Cg). 1991 Mathematics Subject Classification. Primary 57R52, 57R50; Secondary 37C05