The Atiyah-Segal Theorem is a fundamental result in equivariant K-Theory that connects topological spaces with group actions to algebraic invariants, specifically offering a way to compute the equivariant K-Theory of a space. This theorem highlights the relationship between stable homotopy theory and representation theory, showing how K-Theory can provide insights into the behavior of vector bundles in the presence of symmetries. It is crucial for understanding Bott periodicity and localization phenomena in equivariant settings.
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