Smooth manifolds and their applications in homotopy theory

The following sections are included:

• Introduction

• Chapter I. Smooth manifolds and their maps

  • Smooth manifolds

  • Embedding of a manifold into Euclidean space

  • Nonproper points of smooth maps

  • Non-degenerate singular points of smooth mappings

• Chapter II. Framed manifolds

  • Smooth approximations of continuous mappings and deformations

  • The basic method

  • Homology group of framed manifolds

  • The suspension operation

• Chapter III. The Hopf invariant

  • Homotopy classification of mappings of n-manifolds to the n-sphere

  • The Hopf invariant of mappings Σ^2k+1 → S^k+1

  • Framed manifolds with Hopf invariant equal to zero

• Chapter IV. Classification of mappings Sⁿ⁺² → Sⁿ

  • The Euclidean space rotation group

  • Classification of mappings Σ³ → S²

  • Classification of mappings from (n + 1)-sphere to n-sphere

  • Classification of mappings Σ⁽ⁿ⁺²⁾ → Sⁿ

• References