Topological and Geometric filtration for products

We show that the Friedlander-Mazur conjecture holds for the product of an elliptic curve with some smooth projective variety of dimension 3. Moreover, we show that the Friedlander-Mazur conjecture is stable under a surjective map. As applications, we show that the Friedlander-Mazur conjecture holds uniruled threefolds and unirational varieties up to certain range.