### Function spaces and continuous algebraic pairings for varieties, by Eric M Friedlander and Mark E Walker

Given a quasi-projective complex variety X and a projective variety
Y, one may endow the set of morphisms, Mor(X,Y), from X to Y
with the natural structure of a topological space. We introduce a
convenient technique (namely, the notion of a functor on the category
of ``smooth curves'') for studying these function complexes and for forming
continuous pairings of such. Building on this technique, we
establish several results, including: (1) the existence of cap and
join product pairings in topological cycle theory, (2) the agreement of
cup product and intersection product for topological cycle theory, (3)
the agreement of the motivic cohomology cup product with morphic
cohomology cup product, and (4) the Whitney sum formula for the Chern
classes in morphic cohomology of vector bundles.

Eric M Friedlander <eric@math.nwu.edu>

Mark E Walker <mwalker@math.unl.edu>