If we consider the homology groups $H_n(X)$ of a topological space $X$—say a CW complex for example—one can interpret every free summand of $H_n(X) \cong \mathbb{Z} ^k \oplus T$ as an $n$-dimensional "hole". Compare with this collecition of informal examples on wikipedia.
If we consider the torsion summand $T$ though, what geometrical/intuitive meaning does this torsion with respect to $X$? For example, what does it mean about $X$ if $T = \mathbb{Z}/(a)$ for $a \neq 1, 0$?
