Memoirs of the American Mathematical Society 1994; 110 pp; softcover Volume: 110 ISBN10: 0821825917 ISBN13: 9780821825914 List Price: US$39 Individual Members: US$23.40 Institutional Members: US$31.20 Order Code: MEMO/110/529
 This work provides a detailed exposition of a classical topic from a very recent viewpoint. Friedlander and Mazur describe some foundational aspects of "Lawson homology" for complex projective algebraic varieties, a homology theory defined in terms of homotopy groups of spaces of algebraic cycles. Attention is paid to methods of group completing abelian topological monoids. The authors study properties of Chow varieties, especially in connection with algebraic correspondences relating algebraic varieties. Operations on Lawson homology are introduced and analyzed. These operations lead to a filtration on the singular homology of algebraic varieties, which is identified in terms of correspondences and related to classical filtrations of Hodge and Grothendieck. Readership Graduate students familiar with algebraic geometry of algebraic topology as well as mathematicians with research interests in algebraic cycles. Table of Contents  Introduction
 Questions and speculations
 Abelian monoid varieties
 Chow varieties and Lawson homology
 Correspondences and Lawson homology
 "Multiplication" of algebraic cycles
 Operations in Lawson homology
 Filtrations
 Appendix A. Mixed Hodge structures, homology, and cycle classes
 Appendix B. Trace maps and the DoldThom theorem
 Appendix Q. On the group completion of a simplicial monoid
 Bibliography
