Semi-topological cycle theory I

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.