论文标题
非招称莫尔斯 - 男性流动和奇怪的chern-weil理论
Non-tame Morse-Smale flows and odd Chern-Weil theory
论文作者
论文摘要
G. Minervini使用Shilnikov在六十年代提出的一定良好的颂歌问题，在他的博士学位论文[17]中证明了Harvey-Lawson对角定理，但没有摩尔斯摩尔斯流动的限制性驯服条件。在这里，我们将相同的技术与Latschev的想法相结合，以构建纤维捆绑包部分的局部分辨率。这是一个垂直矢量场，在每个纤维中都在水平恒定且摩尔斯山脉。该分辨率允许在[3]中从同质公式中取出驯服假设。我们提供一个有限的和一个无限的维度应用。为此，我们引入了与由Hermitian矢量束，单一的内态和度量兼容连接组成的任何三重（E; u; \ nabla）相关的奇数奇数的封闭平滑形式。
Using a certain well-posed ODE problem introduced by Shilnikov in the sixties, G. Minervini proved in his PhD thesis [17], among other things, the Harvey-Lawson Diagonal Theorem but without the restrictive tameness condition for Morse flows. Here we combine the same techniques with the ideas of Latschev in order to construct local resolutions for the flow of the graph of a section of a fiber bundle. This is endowed with a vertical vector field which is horizontally constant and Morse-Smale in every fiber. The resolution allows the removal of the tameness hypothesis from the homotopy formula in [3]. We give one finite and one infinite dimensional application. For that end, we introduce closed smooth forms of odd degree associated to any triple (E;U;\nabla) composed of a hermitian vector bundle, unitary endomorphism and metric compatible connection.
