Stacky Hamiltonian Actions and Symplectic Reduction-Reference-Cited by-同舟云学术

Stacky Hamiltonian Actions and Symplectic Reduction

Published:2020-03-11 Issue:20 Volume:2021 Page:15209-15300
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Hoffman Benjamin¹,Sjamaar Reyer¹

Affiliation:

1. Department of Mathematics, Cornell University, Ithaca, NY 14853-4201, USA

Abstract

Abstract We introduce the notion of a Hamiltonian action of an étale Lie group stack on an étale symplectic stack and establish versions of the Kirwan convexity theorem, the Meyer–Marsden–Weinstein symplectic reduction theorem, and the Duistermaat–Heckman theorem in this context.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2021/20/15209/40739877/rnz322.pdf

Reference51 articles.

1. Higher-dimensional algebra V: 2-groups;Baez;Theory Appl. Categ.,2004

2. Nonrational symplectic toric reduction;Battaglia;J. Geom. Phys.,2019

3. Differentiable stacks and gerbes;Behrend;J. Symplectic Geom.,2011

4. Lie 2-algebras of vector fields;Berwick-Evans;eprint,2016

5. Stacky Lie groups;Blohmann;Int. Math. Res. Not.,2008

Cited by 9 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Shifted Contact Structures on Differentiable Stacks;International Mathematics Research Notices;2024-07-05

2. Morse theory on Lie groupoids;Mathematische Zeitschrift;2024-05-31

3. Riemannian foliations and geometric quantization;Journal of Geometry and Physics;2024-04

4. Isometric Lie 2-Group Actions on Riemannian Groupoids;The Journal of Geometric Analysis;2023-07-27

5. Shifted symplectic higher Lie groupoids and classifying spaces;Advances in Mathematics;2023-01