In their article Instanton counting and Donaldson invariants the authors define the slant product for $\beta \in H_i(X)$ (where $X$ is a manifold) as following.
Let $P \to X$ and SO(3) bundle and $M(P)$ the moduli space of irreducible anti-self-dual connections. Let $\mathcal{P}$ be the universal bundle $X \times M(P)$, then the slant product is defined as: $$ \mu(\beta) := -\frac{1}{4}p_1(\mathcal{P})/\beta $$ This in the end of page 5. What does it even mean to divide by a homology class?