Homotopy groups of spheres

Homotopy groups of spheres are a fundamental topic in algebraic topology that encapsulate information about the topology of higher-dimensional spheres. More formally, the \(n\)-th homotopy group of the \(n\)-dimensional sphere \(S^n\), denoted \(\pi_n(S^n)\), is defined as the set of homotopy classes of based continuous maps from the \(n\)-dimensional sphere \(S^n\) to itself.