论文标题
Bott-Thom同构，Hopf捆绑和摩尔斯理论
Bott-Thom isomorphism, Hopf bundles and Morse theory
论文作者
论文摘要
基于对路径空间的能量功能的摩尔斯理论，我们开发了一个变形理论，用于将球体的映射空间映射到正交组中。这用于表明这些映射空间在稳定范围内与与正交Clifford相关的映射空间相当的弱同质性等效物。 Given an oriented Euclidean bundle $V \to X$ of rank divisible by four over a finite complex $X$ we derive a stable decomposition result for vector bundles over the sphere bundle $\mathord{\mathbb S}( \mathbb{R} \oplus V)$ in terms of vector bundles and Clifford module bundles over $X$.在传递拓扑K理论之后，这些结果暗示了经典的胸部thom同构定理。
Based on Morse theory for the energy functional on path spaces we develop a deformation theory for mapping spaces of spheres into orthogonal groups. This is used to show that these mapping spaces are weakly homotopy equivalent, in a stable range, to mapping spaces associated to orthogonal Clifford representations. Given an oriented Euclidean bundle $V \to X$ of rank divisible by four over a finite complex $X$ we derive a stable decomposition result for vector bundles over the sphere bundle $\mathord{\mathbb S}( \mathbb{R} \oplus V)$ in terms of vector bundles and Clifford module bundles over $X$. After passing to topological K-theory these results imply classical Bott-Thom isomorphism theorems.
