# Cohomology of weighted projective spaces

Suppose that $a,b,c$ are positive integers such that $gcd(a,b,c) = 1$. Let $X$ be the complex weighted projective space $\mathbb{C} \mathbb{P}(1,a,b,c)$. How to compute the group $T(H^{3}(X,\mathbb{Z}))$?

Notation: If $A$ is an abelian group then $T(A)$ denotes the torsion subgroup.