2018/07/22 by Pedro Frejlich · 12 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Topics in Algebra #Algebra over a field #Cohomology #Context (archaeology) #Homotopy #Homotopy and Cohomology in Algebraic Topology #Lie algebra #Lie algebroid #Mathematics #Pure mathematics #Sphingolipid Metabolism and Signaling #math.SG
paper · pdf · doi:10.1016/j.geomphys.2018.12.011
published in Journal of Geometry and Physics 137, 237-246 (Elsevier BV) · 10 pages. Comments are welcome
arxiv created 2018/07/22 · openalex publication_date 2018/12/21 · arxiv updated 2019/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this note, we examine the bundle picture of the pullback construction of Lie algebroids. The notion of submersions by Lie algebroids is introduced, which leads to a new proof of the local normal form for lie algebroid transversals of [Bursztyn et al., Crelle, 2017], and which we use to deduce that Lie algebroids transversals concentrate all local cohomology. The locally trivial version of submersions by Lie algebroids \mathfrakS is then discussed, and we show that this notion is equivalent to the existence of a complete Ehresmann connection for \mathfrakS, extending the main result in [del Hoyo, Indag. Math. 2016]. Finally, we show that locally trivial version of submersions by Lie algebroids gives rise to a system of local coefficients, which is an integral part of a version of the homotopy invariance of de Rham cohomology in the context of Lie algebroids, and we apply such local systems to extend the localization theorem of [Chen et al. 2006].