Algebraic cycles and Lawson homology

This thesis is a collection of several independent results in theory of algebraic cycles and Lawson homology. In Chapter One, new birational invariants are defined by Lawson homology. In Chapter Two, we prove that the Generalized Hodge Conjecture is a birationally invariant statement for 1-cycles and codimension two algebraic cycles for smooth projective varieties. In Chapter Three, we obtain new relations between the geometric filtration and topological filtration on the integral cohomology of a smooth projective variety. We partially prove the Friedlander-Mazur Conjecture in lower dimensions. In Chapter Four, we get to a dual result of C. Peters. In Chapter Five, we construct some rational 4-dimensional projective varieties which carry infinitely generated Lawson homology groups. We also construct two rational 3-dimensional projective varieties which have the same homeomorphism type but different Lawson homology. In Chapter Six, we generalize the Griffiths' Abel-Jacobi map to Lawson homology and give examples of smooth projective varieties which have infinitely generated Lawson homology groups. In Chapter Seven, we generalize the result in Chapter Six, i.e., we defined a map from Lawson homology to Deligne Cohomology.;Each chapter is a self-contained paper. Some chapters of this thesis have been put on the web of preprints: http://www.arxiv.org.