On triangulations of orbifolds and formality
type: Item
instance of: scholarly article
title: On triangulations of orbifolds and formality
zbMATH Open document ID: 1502.57019
author: Yanyan Li
published in: Annals of Global Analysis and Geometry
publication date: 2022-10-13T00:00:00Z
review text: Orbifolds are generalizations of manifolds, locally they are quotients of Euclidean spaces by smooth actions of finite groups. The underlying space of an orbifold can be stratified by the isotropy types, and it admits a triangulation as a stratified space. Orbifolds are naturally associated with two differential graded algebras. One of them is the DGA of orbifold differential forms, i.e., the orbifold de Rham algebra. If the underlying space of the orbifold admits a smooth triangulation, there is also the DGA of piecewise polynomial differential forms of the triangulation. The authors show that these two DGAs are weakly equivalent, which means that they are connected by a chain of quasi-isomorphisms. It follows that one of these DGAs is formal, if and only if the other one is. The authors also prove that global quotient orbifolds and global homogeneous isotropy orbifolds admit smooth triangulations.
reviewed by: Marja Kankaanrinta
Mathematics Subject Classification ID: 57R18
Mathematics Subject Classification ID: 55U10
zbMATH DE Number: 7601375
zbMATH Keywords: orbifolds
zbMATH Keywords: smooth triangulation
zbMATH Keywords: formality
Wikidata QID: Q114227697
MaRDI profile type: Publication
full work available at URL: s10455-022-09874-w
OpenAlex ID: W4295864684
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DOI: 10.1007/S10455-022-09874-W
description: scientific article; zbMATH DE number 7601375