Consider homology and cohomology of some space $X$ where the homology groups are finitely generated. Consider $tor(H^i(X))$, the torsion part of $H^i(X)$.
How do the generators of $tor(H^i(X))$ relate to the generators of $H_{i-1}(X)$ in the Universal Coefficient Theorem?
Is there a way of espressing the generators of $tor(H^i(X))$ in terms of the generators of $H_{i-1}(X)$, maybe an expression of the generators on the chain and cochain level?