Bündelisomorphismus

Bündelisomorphismus, also known as bundle isomorphism, is a concept in mathematics, specifically in the field of differential geometry and topology. It refers to an isomorphism between two fiber bundles, which are mathematical structures consisting of a total space, a base space, and a fiber space, along with a projection map that relates these spaces.

An isomorphism between two fiber bundles is a bijective map that preserves the bundle structure. This means that the map respects the projection onto the base space and the fiber structure. In other words, it maps each fiber of one bundle to a fiber of the other bundle in a way that is consistent with the bundle's projection map.

Bündelisomorphismus is a fundamental concept in the study of fiber bundles and has applications in various areas of mathematics, including differential topology, algebraic geometry, and theoretical physics. It is used to classify fiber bundles up to isomorphism and to study the properties of fiber bundles and their associated geometric structures.