arXiv2026
We establish a decomposition of integral Lawson homology compatible with cycle class maps for projective varieties filtered by Zariski locally trivial affine space bundles over smooth projective bases. Resolving the graph closures produces liftings without a flatness assumption on the graph projections. We prove that these liftings are independent of the chosen resolutions and yield compatible projectors and filtrations on Lawson homology and singular homology. When the bases have dimension at most two, the comparison maps are injective, are isomorphisms in degrees $k>2p$, and have torsion free diagonal cokernels determined by the surface bases. In this case all integral Hodge homology classes are algebraic. For smooth projective varieties with a multiplicative group action and fixed components of dimension at most two, the ranks of the diagonal cokernels form a symmetric polynomial. We also describe the change of this polynomial under blow-ups and compute it for rational varieties obtained by blowing up quartic surfaces. We recover the known smooth motivic decomposition and distinguish its consequences from these refinements. Applications include cones, singular hypersurfaces, toric varieties, finite quotients, symmetric products, and Hilbert schemes of points on surfaces with integral Tate motives.