论一种新的几何同调理论及其在范畴Gromov-Witten理论中的应用
On a new geometric homology theory and an application in categorical Gromov-Witten theory
AI总结：
本文证明带角光滑orbifold可三角剖分，并据此提出几何同调理论GHT以克服奇异同调的组合刚性，同时展示其在范畴Gromov-Witten理论中的应用。
摘要：
本文目的有二：1. 我们证明带角光滑orbifold的可三角剖分性，推广了orbifold的相应结论。2. 基于1，我们提出一种新的同调理论，称之为几何同调理论（简称GHT）。GHT是奇异同调的一种自然且灵活的推广。它具有一些优势，可克服奇异同调令人不快的组合刚性，例如沿纤维丛的奇异链拉回定义不良的问题。我们使用的方法主要基于著名的Lie群胚及其轨道空间的分层与三角剖分理论，以及我们对带角Lie群胚的推广。我们展示GHT在由Costello开创的范畴Gromov-Witten理论中的一个简单应用。我们将在后续论文中进一步发展该理论。
英文摘要：
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.
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