Year: 2022
Type: preprint
Abstract: The purpose of this paper is to investigate the definition of symplectic structure on a smooth stratified pseudomanifold in the framework of local $\C^{\infty}$-ringed space theory. We introduce a sheaf-theoretic definition of symplectic form and cohomologically symplectic structure on smooth stratified pseudomanifolds. In particular, we give an indirect definition of symplectic form on the quotient space of a smooth $G$-stratified pseudomanifold. Based on the structure theorem of singular symplectic quotients by Sjamaar--Lerman, we show that the singular reduced space $M_{0}=μ^{-1}(0)/G$ of a symplectic Hamiltonian $G$-manifold $(M,ω,G,μ)$ admits a natural (indirect) symplectic form and a unique cohomologically symplectic structure.
Source: arXiv (Cornell University)
Author: Yang, Xiangdong
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4301037591