Citation/Abstract

We compute Lawson homology groups and semi-topological K-theory for certain "degenerate" varieties. "Degenerate" varieties are those smooth complex projective varieties whose zero cycles are supported on a proper subvariety. Rationally connected varieties are examples of such varieties. Our main method of study makes use of a technique of Bloch and Srinivas, of the Bloch-Kato conjecture and of the spectral sequence relating morphic cohomology and semi-topological K-theory. In the end of the thesis we focus on the understanding of Lawson homology of generic hypersurfaces of small degree. Our method is based on the fact that for a certain class of hypersurfaces the cylindrical correspondence homomorphism on Lawson homology is a surjection and it is an extension of a method first used by J. Lewis in his study of Chow groups of small degree hypersurfaces.