  We construct a geometric cycle model for a Hodge filtered extension of
complex cobordism for every smooth manifold with a filtration on its de Rham
complex with complex coefficients. Using a refinement of the Pontryagin-Thom
construction, we construct an explicit isomorphism between our geometric model
and the abstract model of Hodge filtered complex cobordism of Hopkins-Quick for
every complex manifold with the Hodge filtration.
