Topology of Lie groups refers to the study of the topological structures and properties of Lie groups, which are groups that are also differentiable manifolds. The intersection of group theory and differential geometry, this area is essential for understanding how the algebraic and geometric aspects of Lie groups interact.
Topology of homogeneous spaces is a concept in mathematics that primarily arises in the field of differential geometry and algebraic topology. A **homogeneous space** is a type of space that looks "the same" at every point, meaning it can be acted upon transitively by a group of symmetries (often a Lie group).
Bott periodicity theorem is a central result in stable homotopy theory, named after the mathematician Raoul Bott. The theorem essentially states that the homotopy groups of certain topological spaces exhibit periodic behavior. More specifically, Bott periodicity is concerned with the stable homotopy groups of spheres and the stable homotopy classification of certain types of vector bundles.
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