On the equivalence of the integrability obstructions for transitive Lie algebroids
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910097177837568 |
|---|---|
| author | Antonini, Paolo Giannotta, Alessio |
| author_facet | Antonini, Paolo Giannotta, Alessio |
| contents | The integrability problem for transitive Lie algebroids can be looked at from different perspectives, revealing an interplay between cohomological methods and homotopical constructions. Mackenzie introduced a cohomological obstruction defined via sheaf-theoretic methods. On the other hand, Crainic and Fernandes used a path space approach and characterized integrability in terms of the monodromy. Recently, Meinrenken formulated the monodromy in terms of a clutching construction.
We show that all of these agree. In particular, we identify the monodromy map with the Mackenzie obstruction class through the natural pairing between cohomology and homotopy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01839 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the equivalence of the integrability obstructions for transitive Lie algebroids Antonini, Paolo Giannotta, Alessio Differential Geometry Algebraic Topology Symplectic Geometry The integrability problem for transitive Lie algebroids can be looked at from different perspectives, revealing an interplay between cohomological methods and homotopical constructions. Mackenzie introduced a cohomological obstruction defined via sheaf-theoretic methods. On the other hand, Crainic and Fernandes used a path space approach and characterized integrability in terms of the monodromy. Recently, Meinrenken formulated the monodromy in terms of a clutching construction. We show that all of these agree. In particular, we identify the monodromy map with the Mackenzie obstruction class through the natural pairing between cohomology and homotopy. |
| title | On the equivalence of the integrability obstructions for transitive Lie algebroids |
| topic | Differential Geometry Algebraic Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2604.01839 |