Exercises:Saul - Algebraic Topology - 3/Exercise 3.2

Exercises

Exercise 3.2

Suppose that $(X,\mathcal{ J })$ is a non-empty path-connected topological space, equipped with a $\Delta$-complex structure. Show, directly from the definitions (Hatcher, of course...) that $H^\Delta_0(X)\cong\mathbb{Z}$

• We may assume without proof that the $1$-skeleton is path connected.