A brief introduction to Dirac manifolds

2011/12/21 by Henrique Bursztyn, Bursztyn, Henrique · 8 citations
Arts and Humanities · Social Sciences · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Philosophical Thought and Analysis #Philosophy and Phenomenology Studies #Spanish Philosophy and Literature #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1112.5037

openalex publication_date 2011/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

These notes are based on lectures given at the school on Geometric and Topological Methods for Quantum Field Theory, in Villa de Leyva, Colombia, in 2009. We present a basic introduction to Dirac manifolds, recalling the original context in which they were defined, their main features, and briefly mentioning more recent developments.

Cited by

• Dirac geometry, deformation theory and shifted symplectic geometry
• F-manifolds, F_man-algebras and Poisson-algebra Distributions
• Mixed superposition rules for Lie systems and compatible geometric structures
• Hamiltonian reduction from particular integrals
• Hamiltonian actions on 0-shifted cosymplectic groupoids
• A note on pullbacks and blowups of Lie algebroids, singular foliations, and Dirac structures
• On the geometry of complex Poisson bivectors
• Blowups of Dirac structures

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