Work

The shifted symplectic geometry of derived higher groupoids

Year: 2026

Type: preprint

Abstract: The main goal of this work is to introduce derived Lie n-groupoids and their shifted symplectic structures. We further define shifted lagrangian structures and prove that their composition is well defined under suitable conditions. As an application, we show that our framework incorporates several reduction procedures at critical values, including: classical Hamiltonian reduction, group valued moment maps, Poisson Lie group valued moment maps and Mikami-Weinstein for proper symplectic groupoids.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2607.17362

Authors: Cueca, Miquel, Dorsch, Florian, Sjamaar, Reyer, Zhu, Chenchang

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7169876162

Cites: 16

Cited by: 1

Related to: 10