发表机构
School of Mathematics, Nanjing University; College of Mathematics and Systems Science, Shandong University of Science and Technology（南京大学数学系; 山东科技大学数学与系统科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究定义了加权多面体的概念，构建了其加权奇异同调理论并证明其与加权单纯同调同构，还推广了相关上同调乘积并阐释了orbifold理论。
AI 中文摘要
我们定义了加权多面体的概念，可将其视为Dawson引入的加权单纯复形的几何实现。此外，我们将为加权多面体定义奇异同调理论的加权版本，并证明其与加权多面体的加权单纯同调同构。这意味着加权单纯同调是同构下的不变量，更一般地，是加权多面体在特定类型同伦等价下的不变量。我们还将杯积和帽积推广到加权奇异上同调，并从我们的加权奇异同调与上同调的角度阐释一些已知的orbifold理论。
英文摘要
We define the notion of weighted polyhedron which can be thought of as the geometric realization of a weighted simplicial complex introduced by Dawson. Moreover, we will define a weighted version of singular homology theory for a weighted polyhedron and prove that it is isomorphic to the weighted simplicial homology of the weighted polyhedron. This implies that weighted simplicial homology is an invariant under isomorphisms and more generally under certain type of homotopy equivalences of weighted polyhedra. Moreover, we will generalize the cup product and cap product to weighted singular cohomology. In addition, we will interpret some known theories of orbifolds in terms of our weighted singular homology and cohomology.
Comments46 pages, 7 figures, some contents overlap with arXiv:2106.06794
