A note on pullbacks and blowups of Lie algebroids, singular foliations, and Dirac structures

2025/09/03 by Schüßler, Andreas, Zambon, Marco
#Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2509.03698

Abstract

Lie algebroids, singular foliations, and Dirac structures are closely related objects. We examine the relation between their pullbacks under maps satisfying a constant rank or transversality assumption. A special case is given by blowdown maps. In that case, we also establish the relation between the blowup of a Lie algebroid and its singular foliation.

Citations

• The blow-down map in Lie algebroid cohomology
• Knots, minimal surfaces and J-holomorphic curves
• Blow-ups of Lie groupoids and Lie algebroids
• Coregular submanifolds and Poisson submersions
• Blowup constructions for Lie groupoids and a Boutet de Monvel type calculus
• Symplectic groupoids of log symplectic manifolds
• A brief introduction to Dirac manifolds

Cited by

• Blowups of Dirac structures

Related

• A duality between Lie algebroids and infinitesimal foliations
• The blow-down map in Lie algebroid cohomology
• Blow-ups of Lie groupoids and Lie algebroids
• Generalizing Geometry - Algebroids and Sigma Models
• Blowups of Dirac structures