Chern classes

Chern classes are mathematical tools used in geometry and topology to measure how complex shapes and spaces twist or curve. Imagine a surface or a higher-dimensional object; Chern classes help quantify how the shape's structure changes when viewed from different angles or stretched. They provide algebraic invariants that encapsulate this curvature and twisting, allowing mathematicians to classify and understand subtle geometric properties in a formal way. Essentially, Chern classes serve as a bridge between geometry and algebra, offering a way to study the shape's intrinsic features.