Raoul BottRaoul Bott, né le et mort le , est un mathématicien connu pour nombre de contributions en géométrie. Né à Budapest, il passe l'essentiel de sa vie aux États-Unis. Sa famille émigre au Canada en 1938 à la veille de la Seconde Guerre mondiale. Il étudie à l'université McGill. Il devient professeur à Harvard en 1958, et il y enseigne jusqu'en 1999. Il meurt du cancer à San Diego en 2005. Son travail porte initialement sur la physique avant de se tourner vers les mathématiques pures.
Fiber bundle construction theoremIn mathematics, the fiber bundle construction theorem is a theorem which constructs a fiber bundle from a given base space, fiber and a suitable set of transition functions. The theorem also gives conditions under which two such bundles are isomorphic. The theorem is important in the associated bundle construction where one starts with a given bundle and surgically replaces the fiber with a new space while keeping all other data the same. Let X and F be topological spaces and let G be a topological group with a continuous left action on F.
Dual bundleIn mathematics, the dual bundle is an operation on vector bundles extending the operation of duality for vector spaces. The dual bundle of a vector bundle is the vector bundle whose fibers are the dual spaces to the fibers of . Equivalently, can be defined as the Hom bundle that is, the vector bundle of morphisms from to the trivial line bundle Given a local trivialization of with transition functions a local trivialization of is given by the same open cover of with transition functions (the inverse of the transpose).
SubmanifoldIn mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S → M satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required. Different authors often have different definitions. In the following we assume all manifolds are differentiable manifolds of class Cr for a fixed r ≥ 1, and all morphisms are differentiable of class Cr.
