On page 132 of "Introduction to Supergravity" by Horiatiu Nastase, the author says:

On $M = CY_3$ (Calabi-Yau space) there are $b_3$ topologically nontrivial 3-surfaces, for which we can define a basis $(A_I, B^J)$, where $I, J = 1, \ldots, b_3/2$, such that $A_I \cap A_J = B^I \cap B^J = 0$ and $A_I \cap B^J = -B^J \cap A_I = \delta_I^J$.

What does the intersection symbol denote here? I understand that $A_I$ and $B^J$ are $(b_3/2, 0)$ and $(0, b_3/2)$ forms.

What does the minus sign in $A_I \cap B^J = -B^J \cap A_I = \delta_I^J$ mean?

On page 132 of "Introduction to Supergravity" by Horiatiu Nastase, the author says:

On $M = CY_3$ (Calabi-Yau space) there are $b_3$ topologically nontrivial 3-surfaces, for which we can define a basis $(A_I, B^J)$, where $I, J = 1, \ldots, b_3/2$, such that $A_I \cap A_J = B^I \cap B^J = 0$ and $A_I \cap B^J = -B^J \cap A_I = \delta_I^J$.

What does the intersection symbol denote here? I understand that $A_I$ and $B^J$ are $(b_3/2, 0)$ and $(0, b_3/2)$ forms.

What does the minus sign in $A_I \cap B^J = -B^J \cap A_I = \delta_I^J$ mean?