论文标题
稳定的Pontryagin- Thom Thom构造适当地图II
Stable Pontryagin-Thom construction for proper maps II
论文作者
论文摘要
在Arxiv：1905.07734中，我们提出了一种结构，该结构是Pontryagin's的类似物，用于稳定尺寸的适当地图。这在给定的歧管$ w $的$ w \ times \ times \ mathbb {r}^n $中的框架嵌入式紧凑型子手机的共同体之间进行了两次培训，对于给定的歧管$ w $和足够大的数字$ n $，与$ w \ w \ w \ w \ times \ times \ times \ mathbb {r}^n $ to $ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ n $的合格类别类别在本文中，我们以与汤姆（Thom）的构造通用蓬蒂（Pontryagin）相似的方式概括了这一结果。换句话说，我们在$ w \ times \ times \ mathbb {r}^n $中嵌入的submanifolds集合之间进行了两者的培养，并从给定的捆绑包$ξ\ oplus \ oplus \ oplus \ varepsilon^n $中引起的正常捆绑$ u（ξ\ oplus \ varepsilon^n）$，取决于给定的捆绑包。汤姆（Thom）的构建与我们的建设之间的重要区别在于，我们还考虑了对这些合适的恢复性关系的概念后，我们还考虑了非紧凑型歧管的共同体。
In arXiv:1905.07734 we presented a construction that is an analogue of Pontryagin's for proper maps in stable dimensions. This gives a bijection between the cobordism set of framed embedded compact submanifolds in $W\times\mathbb{R}^n$ for a given manifold $W$ and a large enough number $n$, and the homotopy classes of proper maps from $W\times\mathbb{R}^n$ to $\mathbb{R}^{k+n}$. In the present paper we generalise this result in a similar way as Thom's construction generalises Pontryagin's. In other words, we present a bijection between the cobordism set of submanifolds embedded in $W\times\mathbb{R}^n$ with normal bundles induced from a given bundle $ξ\oplus\varepsilon^n$, and the homotopy classes of proper maps from $W\times\mathbb{R}^n$ to a space $U(ξ\oplus\varepsilon^n)$ that depends on the given bundle. An important difference between Thom's construction and ours is that we also consider cobordisms of non-compact manifolds after indroducing a suitable notion of cobordism relation for these.
