Algebraic Cycles and Lawson Homology

The fundamental object of interest in algebraic geometry isthe structure of spaces of algebraic cycles on a projectivevariety. Any profound understanding of this will be very helpful toknow the structure of projective manifolds. The study of algebraiccycles may date back to 1930s. A breakthrough of the homotopytheoretic approach to algebraic cycles is the Algebraic SuspensionTheorem proved by Blaine Lawson in the late 1980s. This method hasbeen developed by Eric Friedlander, Blaine Lawson and others. Thisbook studies further properties of Lawson homology as well asrelations to the singular homology and Chow groups. In particular,new nontrivial birational invariants for complex smooth projectivevarieties are defined using Lawson homology; Birational invariantstatements for 1-cycles and codimension two cycles are given;Generalized Abel-Jacobi map for Lawson homology is constructed;Examples of both smooth and singular projective varieties areconstructed to hold infinitely generated Lawson homology groupseven up to torsion. It is suitable for those interested in complexalgebraic geometry, especially the homotopy theoretic aspect ofalgebraic cycles theory.