On nontriviality of homotopy groups of spheres

TL;DR

This paper discusses the nontrivial nature of homotopy groups of spheres, specifically showing that for all n ≥ 2, the homotopy groups of the 2-sphere are non-zero, highlighting their complex structure.

Contribution

It establishes the nontriviality of homotopy groups of spheres for all n ≥ 2, emphasizing their fundamental role in algebraic topology.

Findings

Homotopy groups π_n(S^2) are non-zero for all n ≥ 2.

The nontriviality of these groups indicates complex topological properties.

Supports the understanding of sphere topology in higher dimensions.

Abstract

For $n\geq 2$, the homotopy groups $\pi_n(S^2)$ are non-zero.