论文标题
循环后，球体捆绑超过$ 4 $ -Manifolds是微不足道的
Sphere bundles over $4$-manifolds are trivial after looping
论文作者
论文摘要
我们表明，除两种特殊情况外，循环后的简单连接$ 4 $ manifold拆分的矢量捆绑包的球体捆绑包。特别是，这意味着，尽管有无限的不等球体捆绑范围超过$ 4 $ - manifold，但其总歧管的环空间都是同等的。
We show that except two special cases, the sphere bundle of a vector bundle over a simply connected $4$-manifold splits after looping. In particular, this implies that though there are infinitely many inequivalent sphere bundles of a given rank over a $4$-manifold, the loop spaces of their total manifolds are all homotopy equivalent.
