论文标题
悬挂$ 4 $ - manifolds的同副型类型
Homotopy Types of Suspended $4$-manifolds
论文作者
论文摘要
给定一个封闭，平稳，连接，可取向的$ 4 $ - manifold $ m $，其整体同源组可以具有$ 2 $ torsion，我们确定双重悬架$σ^2M $的同质拷贝分解为某些基本$ \ \ m mathbf {a a} a} _3^3 $ complexes $ 2 $ 2 $ 2的$ connite $ connite $ connite $ connite $ connite $ connite $ connite $ connite $ connite。此外，我们利用后尼科夫广场（或等效的pontryagin Square）为$σ^2M $的同型分解找到足够的条件，从而将其删除至$σm$。
Given a closed, smooth, connected, orientable $4$-manifold $M$, whose integral homology groups can have $2$-torsion, we determine the homotopy decomposition of the double suspension $Σ^2M$ as wedge sums of some elementary $\mathbf{A}_3^3$-complexes, which are $2$-connected finite complexes of dimension at most $6$. Furthermore, we utilize the Postnikov square (or equivalently Pontryagin square) to find sufficient conditions for the homotopy decompositions of $Σ^2M$ to desuspend to that of $ΣM$.
