“Stable Prime Decompositions of Four-Manifolds” by
“Stable Prime Decompositions of Four-Manifolds” by
复制标题
“四流形的稳定素数分解” 作者：
DOI：
--
复制
发表时间：
2003
期刊：
影响因子：
--
通讯作者：
P. Teichner
中科院分区：
文献类型：
--
作者：
M. Kreck;W. Lück;P. Teichner
本文的主要结果是一个四维稳定版本的Kneser猜想分裂的三维流形作为连通和。即设M是拓扑分别光滑的紧连通四流形（具有定向或自旋结构）。假设π1（M）分裂为π i=1Γi，使得π1（C）在π1（M）中的像对于π 1（M）的每个分量C亚共轭到某个Γi。则M分别稳定同胚（保持方向或自旋结构）到一个连通和[i=1Mi，其中Γi = π1（Mi）.稳定意味着允许在两边都有一些S2 × S2的副本的额外连通和。我们还证明了一个唯一性声明。作为结果，我们得到了紧致连通四流形（具有定向或自旋结构）的稳定素分解的存在性和唯一性。主要的技术成分是bordism方法的稳定分类的流形由于第一作者和Kurosh子群定理。
The main result of this paper is a four-dimensional stable version of Kneser’s conjecture on the splitting of three-manifolds as connected sums. Namely, let M be a topological respectively smooth compact connected four-manifold (with orientation or Spin-structure). Suppose that π1(M) splits as ∗i=1Γi such that the image of π1(C) in π1(M) is subconjugated to some Γi for each component C of ∂M . Then M is stably homeomorphic respectively diffeomorphic (preserving the orientation or Spin-structure) to a connected sum ]i=1Mi with Γi = π1(Mi). Stably means that one allows additional connected sums with some copies of S2 × S2 on both sides. We also prove a uniqueness statement. As a consequence we obtain the existence and uniqueness of the stable prime decomposition of compact connected four-manifolds (with orientation or Spin-structure). The main technical ingredients are the bordism approach to the stable classification of manifolds due to the first author and the Kurosh Subgroup Theorem.