Gluing principle for orbifold stratified spaces

Bohui Chen*, An Min Li, Bai Ling Wang

*Corresponding author for this work

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    6 Citations (Scopus)


    In this paper, we explore the theme of orbifold stratified spaces and establish a general criterion for them to be smooth orbifolds. This criterion utilizes the notion of linear stratification on the gluing bundles for the orbifold stratified spaces. We introduce a concept of good gluing structure to ensure a smooth structure on the stratified space. As an application, we provide an orbifold structure on the coarse moduli space Mg,n of stable genus g curves with n-marked points. Using the gluing theory for Mg,n associated to horocycle structures, there is a natural orbifold gluing structure on Mg,n. We show this gluing atlas can be refined to provide a good orbifold gluing atlas and hence a smooth orbifold structure on Mg,n. This general gluing principle will be very useful in the study of the gluing theory for the compactified moduli spaces of stable pseudo-holomorphic curves in a symplectic manifold.

    Original languageEnglish
    Title of host publicationGeometry and Topology of Manifolds - 10th China-Japan Geometry Conference, 2014
    EditorsReiko Miyaoka, Akito Futaki, Weiping Zhang, Zizhou Tang
    PublisherSpringer New York LLC
    Number of pages43
    ISBN (Print)9784431560197
    Publication statusPublished - 2016
    Event10th Geometry Conference on Friendship between China and Japan, 2014 - Shanghai, China
    Duration: 7 Sept 201411 Sept 2014

    Publication series

    NameSpringer Proceedings in Mathematics and Statistics
    ISSN (Print)2194-1009
    ISSN (Electronic)2194-1017


    Conference10th Geometry Conference on Friendship between China and Japan, 2014


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