# Tag Archives: exotic sphere

## The Poincare conjecture

The next few sections of Chapter 1 are intended to introduce some key examples of constructions with manifolds: The high-dimensional Poincaré conjecture and the h-cobordism theorem Milnor’s exotic spheres Variation of Pontrjagin classes within a homotopy type In the version … Continue reading

In the previous post I mentioned the two categories of manifolds with which we’re going to be mostly concerned: smooth manifolds, equipped with an atlas whose transition maps are $$C^\infty$$, and topological manifolds (locally Euclidean spaces).  Smooth manifolds are, of … Continue reading