### Exercises #6 – Climbing Algebraic Topology – #4

As a reference, we permit the use of homotopy theorems established in Topology and Geometry [Bredon1993] up till The Whitehead theorem. Exercise 1.Solution.Exercise 1. Let \(n\geq 2\) and let \(X\) be a homology \(n\)-sphere. If \(X\) is a simply-connected CW-complex, show that \(X\simeq \S^n\). Solution. Since \(X\) is simply-connected, by inverse Hurewicz, there is an…