Abstract
We study algebraic varieties parametrized by topological spaces and enlarge the domain of Lawson homology and morphic cohomology to this category. We prove a Lawson suspension theorem and a splitting theorem. A version of the Friedlander‐Lawson moving lemma is obtained to prove a duality theorem between Lawson homology and morphic cohomology for smooth semi-topological projective varieties. K -groups for semi-topological projective varieties and Chern classes are also constructed.
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