Do orientation preserving diffeomorphisms preserve homological intersection?

Let $$M$$ be a $$4$$- dimensional oriented manifold and let D be a 2-dimensional submanifold. Is it true that any $$\phi \in \text{Diff}^+(M)$$(the set of orientation preserving diffeomorphisms) preserves homological intersection i.e $$[D] \cdot [D] = \phi_{*}[D] \cdot \phi_{*}[D]$$.

• Thank you. Just wanted to further know how do you go about showing the claim that $[\phi_{*}(D)] \cdot [\phi_{*}(D)] = \phi_{*}([D] \cdot [D])$? – J-holo curve Dec 20 '18 at 1:33
• Poincare duality is natural for orientation preserving diffeomorphisms, and the intersection product is Poincare dual to the cup product. Alternatively; pick transverse representatives and literally push them forward, and the intersection of the pushed forward cycles will be the pushforward of the intersection. – Mike Miller Dec 20 '18 at 1:59