Exercises:Saul - Algebraic Topology - 7/Exercise 7.6

Exercises

Exercises 7.6

Question

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