2022/11/02 by Luca Accornero, Accornero, Luca, Francesco Cattafi +1 · 1 citation
Mathematics · #58A10 #58A15 #58A20 #58H05 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2211.01319
openalex publication_date 2022/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work is a spin-off of an on-going programme which aims at revisiting the original studies of Lie and Cartan on pseudogroups and geometric structures from a modern perspective. Within the framework of Lie groupoids equipped with a special multiplicative form - called Pfaffian groupoids - we focus on principal bibundles and Morita equivalences. In particular, we discuss in details the notion of Pfaffian Morita equivalence, its relation to the gauge construction in the Pfaffian setting, and its interactions with principal actions. We briefly present some examples and applications to transitive pseudogroups of symmetries, which we explored in great detail in arXiv:2211.16639.