Exercises:Saul - Algebraic Topology - 7/Exercise 7.6

Exercises

Exercises 7.6

Question

1. Compute the singular homology groups of $T^2:\eq\mathbb{S}^1\times\mathbb{S}^1$ and of $X:\eq\mathbb{S}^1\vee\mathbb{S}^1\vee\mathbb{S}^2$
2. Prove that $T^2$ and $X$ are not homotopy equivalent spaces