Isotopy of 4-manifolds
Isotopy of 4-manifolds
复制标题
4-流形的同位素
DOI：
10.4310/jdg/1214440552
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发表时间：
1986
影响因子：
2.5
通讯作者：
F. Quinn
中科院分区：
文献类型：
--
作者：
F. Quinn
本文的主要结果是：闭单连通4-流形的模同伦同胚群（“同伦”群）等于H2上二次型的自同构群。单连通闭四维流形与连通曲面之间有相似之处，因为它们都是由简单的代数拓扑数据分类的。曲面由基本群的同构类分类到同胚。利用Z/2中的交形式的同构类和Kirby-Siebenmann不变量，将4-流形分类为同胚流形[3]。类比现在扩展到自同构，在这两种情况下同胚都是由代数结构的诱导自同构分类的。其他结果包括单连通5-流形上的拟体结构的“唯一性”，π4（TOP（4）/O（4））的确定，以及单连通4-流形上有边界的伪合痕定理.
The principal result of this paper is that the group of homeomorphisms mod isotopy (the "homeotopy" group) of a closed simply-connected 4-manifold is equal to the automorphism group of the quadratic form on H2. There is an analogy between simply-connected closed 4-manifolds and connected surfaces, in that they are both classified by simple algebraictopological data. Surfaces are classified up to homeomorphism by the isomorphism class of the fundamental group. The 4-manifolds are classified up to homeomorphism by the isomorphism class of the intersection form and the Kirby-Siebenmann invariant in Z/2 [3]. The analogy now extends to automorphisms, in that in both cases homeomorphisms are classified by the induced automorphism of the algebraic structure. Other results include a " uniqueness" for handlebody structures on simplyconnected 5-manifolds, the determination of π4(TOP(4)/O(4)), and a pseudoisotopy theorem for simply connected 4-manifolds with boundary.