Atiyah-Bott Localization

Atiyah-Bott Localization is a mathematical principle used in geometry and topology. It simplifies complex integrals over a space by focusing only on points that remain fixed under a symmetry or group action. Instead of analyzing the entire space, it relates the whole to data at these fixed points, making calculations more manageable. Think of it like calculating a map's total elevation change by only examining key landmarks rather than every step in between. This technique is powerful for studying spaces with symmetry, providing elegant solutions to otherwise difficult problems.