  We establish the analogue of the Friedlander-Mazur conjecture for Teh's
reduced Lawson homology groups of real varieties, which says that the reduced
Lawson homology of a real quasi-projective variety $X$ vanishes in homological
degrees larger than the dimension of $X$ in all weights. As an application we
obtain a vanishing of homotopy groups of the mod-2 topological groups of
averaged cycles and a characterization in a range of indices of the motivic
cohomology of a real variety as homotopy groups of the complex of averaged
equidimensional cycles. We also establish an equivariant Poincare duality
between equivariant Friedlander-Walker real morphic cohomology and dos Santos'
real Lawson homology. We use this together with an equivariant extension of the
mod-2 Beilinson-Lichtenbaum conjecture to compute some real Lawson homology
groups in terms of Bredon cohomology.
