On triangulations of orbifolds and formality

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2022-09-08 DOI:10.1007/s10455-022-09874-w

Cheng-Yong Du, Kaimin He, Han Xue

引用次数: 0

Abstract

For an orbifold, there are two naturally associated differential graded algebras, one is the de Rham algebra of orbifold differential forms and the other one is the differential graded algebra of piecewise polynomial differential forms of a triangulation of the coarse space. In this paper, we prove that these two differential graded algebras are weakly equivalent; hence, the formality of these two differential graded algebras is consistent, when the triangulation is smooth. We show that global quotient orbifolds and global homogeneous isotropy orbifolds admit smooth triangulations; hence, the two kinds of formality coincide with each other for these orbifolds.

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论眶的三角形与形式

对于orbifold，有两个自然相关的微分分次代数，一个是orbifold-微分形式的de Rham代数，另一个是粗糙空间三角剖分的分段多项式微分形式的微分分代代数。本文证明了这两个微分分次代数是弱等价的；因此，当三角剖分是光滑的时，这两个微分分次代数的形式是一致的。我们证明了全局商轨道和全局齐次各向同性轨道允许光滑三角；因此，这两种形式对于这些轨道是一致的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.