5 Feb 2024. Talk by Jaime Pedregal at the LIGAT Geometry Seminar, UAB.
Abstract: Lie algebroids can be considered as “adapted tangent bundles” for specific geometric situations. As such, it makes sense to consider Lie algebroid connections and Lie algebroid holonomy. In this talk, after a very brief recap of classical holonomy, we will introduce the notion of Lie algebroids, with examples, and give some intuition on their usefulness. We will then, following the “adapted tangent bundle” philosophy, introduce Lie algebroid holonomy. Two remarkable properties distinguish Lie algebroid holonomy from classical holonomy: the Ambrose–Singer theorem must be enlarged beyond curvature and holonomy can jump from leaf to leaf, with not much control over these jumps. Depending on time we will give examples of both features.