Homotopy groups of spheres using the Pontryagin theorem

Abstract

In this thesis, we discuss the Pontryagin theorem, which states that homotopy groups of spheres are isomorphic to framed cobordism groups. We first introduce homotopy groups and framed cobordism groups. We will be using the regular value theorem and tubular neighbourhood theorem to construct the isomorphism between the two groups. Afterwards, we will discuss a couple of applications.