Cycle Spaces and Intersection Theory
By: Eric M. Friedlander and Ofer Gabber
This paper constitutes a preliminary discussion of joint work in progress as
presented by the first author at Stony Brook in June 1991 at the symposium in
honor of John Milnor. Our results include a construction of an intersection
pairing on spaces of algebraic cycles on a given smooth complex
quasi-projective variety, thereby providing a ring structure in "Lawson
homology." We verify that the Lawson homology for quasi-projective
varieties satisfies sufficiently many of the "standard properites" of a good
homology theory that it admits a theory of Chern classes from algebraic
K-theory. The reader familiar with higher Chow groups of S. Bloch might find
it useful to view Lawson homology as a topological analogue of that theory.
In fact, we exhibit a tantalizing map from Bloch's higher Chow groups to
Lawson homology.
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