Algebraic cycles, Lawson homology and duality

In the beginning of the 90s, Lawson and friedlander introduced a new way of looking at algebraic cycles on a complex algebraic variety via the homotopy type of its moduli space, instead of using the usual Chow groups of cycles modulo an equivalence relation.

In this talk I will describe these semi-topological approach to algebraic
cycles, referring to both, the original work in the 90s and some recent
progress. In particular I will emphasize the Friedlander-Lawson construction of a bivariant theory $M(X,Y)$, cohomological in $X$ and homological in $Y$ and how it leads to the duality theorem, extending Poincaré duality to this context. If time allows, I will end discussing some open problems, and possible directions for the future.