论文标题
关于新的几何同源理论和分类格罗莫夫理论的应用
On a new geometric homology theory and an application in categorical Gromov-Witten theory
论文作者
论文摘要
本文的目的是双重的：1。我们证明了带有角落的光滑轨道的三角测量性，从而概括了相同的orbifolds陈述。 2。基于1，我们提出了一种新的同源理论。我们称其为几何同源理论（缩写为GHT）。 GHT是奇异同源性的自然而灵活的概括。它具有一些优势，克服了奇异同源性的令人不愉快的组合刚度，例如沿纤维束的单数链的不确定的回调。我们使用的方法主要基于lie lie groupoids及其轨道空间的著名分层和三角剖分理论，以及我们与Corners的lie lie groupoid的扩展。我们说明了GHT在由Costello发起的分类Gromov-Witten理论中的简单应用。我们将在续集论文中进一步发展这一理论。
The purpose of this paper is twofold: 1. we prove the triangulability of smooth orbifolds with corners, generalizing the same statement for orbifolds. 2. based on 1, we propose a new homology theory. We call it geometric homology theory (GHT for abbreviaty). GHT is a natural and flexible generalization of singular homology. It has some advantages overcoming the unpleasant combinatoric rigidity of singular homology, e.g. ill-defined pullbacks of singular chains along fiber bundles. The method we use are mainly based on the celebrated stratification and triangulation theories of Lie groupoids and their orbit spaces, as well as the extension to Lie groupoids with corners by us. We illustrate a simple application of GHT in categorical Gromov-Witten theory, initiatied by Costello. We will develop further of this theory in our sequel paper.
