Coloquio Junior de matemáticas
Connections on fiber bundles
Ponente: Matthieu Madera (Université Côte d’Azur, Nice, France)Fecha: miércoles 05 de marzo de 2025 - 17:00 (coffee break: 16:30)Lugar: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Resumen:
The objective of this talk is to present the notion of connection in differential geometry. A connection is a way of comparing the fibers of a fiber bundle via the concept of parallel transport. After defining the concept of fiber bundle, we will introduce horizontal distributions and explain how to transport fibers along curves. We will then focus on vector bundles and linear connections, and explain how a connection is a way of differentiating sections in this context. Finally, we will talk about affine connections and the notions of geodesic spray and exponential map.
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