Gluing principle for orbifold stratified spaces

Bohui Chen; An Min Li; Bai Ling Wang

doi:10.1007/978-4-431-56021-0_2

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 proceeding › Conference contribution › peer-review

6 Citations (Scopus)

Abstract

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 M_g,n of stable genus g curves with n-marked points. Using the gluing theory for M_g,n associated to horocycle structures, there is a natural orbifold gluing structure on M_g,n. We show this gluing atlas can be refined to provide a good orbifold gluing atlas and hence a smooth orbifold structure on M_g,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 language	English
Title of host publication	Geometry and Topology of Manifolds - 10th China-Japan Geometry Conference, 2014
Editors	Reiko Miyaoka, Akito Futaki, Weiping Zhang, Zizhou Tang
Publisher	Springer New York LLC
Pages	15-57
Number of pages	43
ISBN (Print)	9784431560197
DOIs	https://doi.org/10.1007/978-4-431-56021-0_2
Publication status	Published - 2016
Event	10th Geometry Conference on Friendship between China and Japan, 2014 - Shanghai, China Duration: 7 Sept 2014 → 11 Sept 2014

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	154
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	10th Geometry Conference on Friendship between China and Japan, 2014
Country/Territory	China
City	Shanghai
Period	7/09/14 → 11/09/14

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10.1007/978-4-431-56021-0_2

Cite this

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title = "Gluing principle for orbifold stratified spaces",

abstract = "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.",

keywords = "Gluing atlas, Linear stratification, Orbifold stratified space",

author = "Bohui Chen and Li, {An Min} and Wang, {Bai Ling}",

note = "Publisher Copyright: {\textcopyright} Springer Japan 2016.; 10th Geometry Conference on Friendship between China and Japan, 2014 ; Conference date: 07-09-2014 Through 11-09-2014",

year = "2016",

doi = "10.1007/978-4-431-56021-0_2",

language = "English",

isbn = "9784431560197",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "15--57",

editor = "Reiko Miyaoka and Akito Futaki and Weiping Zhang and Zizhou Tang",

booktitle = "Geometry and Topology of Manifolds - 10th China-Japan Geometry Conference, 2014",

}

Chen, B, Li, AM & Wang, BL 2016, Gluing principle for orbifold stratified spaces. in R Miyaoka, A Futaki, W Zhang & Z Tang (eds), Geometry and Topology of Manifolds - 10th China-Japan Geometry Conference, 2014. Springer Proceedings in Mathematics and Statistics, vol. 154, Springer New York LLC, pp. 15-57, 10th Geometry Conference on Friendship between China and Japan, 2014, Shanghai, China, 7/09/14. https://doi.org/10.1007/978-4-431-56021-0_2

Gluing principle for orbifold stratified spaces. / Chen, Bohui; Li, An Min; Wang, Bai Ling.
Geometry and Topology of Manifolds - 10th China-Japan Geometry Conference, 2014. ed. / Reiko Miyaoka; Akito Futaki; Weiping Zhang; Zizhou Tang. Springer New York LLC, 2016. p. 15-57 (Springer Proceedings in Mathematics and Statistics; Vol. 154).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Gluing principle for orbifold stratified spaces

AU - Chen, Bohui

AU - Li, An Min

AU - Wang, Bai Ling

N1 - Publisher Copyright: © Springer Japan 2016.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Gluing atlas

KW - Linear stratification

KW - Orbifold stratified space

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DO - 10.1007/978-4-431-56021-0_2

M3 - Conference contribution

SN - 9784431560197

T3 - Springer Proceedings in Mathematics and Statistics

SP - 15

EP - 57

BT - Geometry and Topology of Manifolds - 10th China-Japan Geometry Conference, 2014

A2 - Miyaoka, Reiko

A2 - Futaki, Akito

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A2 - Tang, Zizhou

PB - Springer New York LLC

T2 - 10th Geometry Conference on Friendship between China and Japan, 2014

Y2 - 7 September 2014 through 11 September 2014

ER -

Gluing principle for orbifold stratified spaces

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