Topological and Geometric filtration for products

We show that the Friedlander-Mazur conjecture holds for a sequence of products of projective varieties such as the product of a smooth projective curve and a smooth projective surface, the product of two smooth projective surfaces, the product of arbitrary number of smooth projective curves. Moreover, we show that the Friedlander-Mazur conjecture is stable under a surjective map. As applications, we show that the Friedlander-Mazur conjecture holds for the Jacobian variety of smooth projective curves, uniruled threefolds and unirational varieties up to certain range.