Chern-Gauss-Bonnet对偶与Lefschetz对偶的一个流观点
Chern-Gauss-Bonnet and Lefschetz Duality from a currential point of view
摘要：
我们使用映射锥的相对deRham上同调的带边流形，以显示，陈-高斯-Bonnet定理定向黎曼向量丛在这样的流形是一个表现的Lefschetz对偶在任何的两个实施方案，后者。我们解释了如何汤姆同构适合这张照片，从而补充了经典的结果，汤姆形式与紧凑的支持。当秩为奇数时，我们利用这里引入的二次海侵形式，构造了一个新的圆盘丛上的闭形式对，它与零截面的一个向量丛对是Lefschetz对偶的.
英文摘要：
We use the mapping cone for the relative deRham cohomology of a manifold with boundary in order to show that the Chern-Gauss-Bonnet Theorem for oriented Riemannian vector bundles over such manifolds is a manifestation of Lefschetz Duality in any of the two embodiments of the latter. We explain how Thom isomorphism fits into this picture, complementing thus the classical results about Thom forms with compact support. When the rank is odd, we construct, by using secondary transgression forms introduced here, a new closed pair of forms on the disk bundle associated to a vector bundle, pair which is Lefschetz dual to the zero section.
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