Two Theorems of Rokhlin

Abstract

Two theorems due to V. A. Rokhlin are proved: the theorem on the third stable homotopy group of spheres: $$\pi _{n + 3} (S^n ) \approx \mathbb{Z}_{24} {\text{ }}for{\text{ }}n \geqslant {\text{5}}$$ ; and the theorem on the divisibility by 16 of the signature of a spin 4-manifold. The proofs use immersion theory. Bibliography 17 titles.