Whitehead product

The Whitehead product is a mathematical operation in algebraic topology that combines two loops or spheres within a space to produce a new element representing how these shapes interact. It captures the way different paths or surfaces in the space can be “commuted” or combined, revealing deeper structural relationships. Essentially, it measures the “twisting” or “linking” of these objects, providing insight into the space’s higher-dimensional features that are not visible through basic analysis. It plays a crucial role in understanding the complex connectivity and structure of topological spaces.