A homology and cohomology theory for real projective varieties Jyh-Haur Teh 14C2514P2555N35algebraic cyclesreal varieties In this paper we develop homology and cohomology theories which play the same role for real projective varieties that Lawson homology and morphic cohomology play for projective varieties respectively. They have nice properties such as the existence of long exact sequences, the homotopy invariance, the Lawson suspension property, the homotopy property for bundle projection, the splitting principle, the cup product, the slant product and the natural transformations to singular theories. The Friedlander-Lawson moving lemma is used to prove a duality theorem between these two theories. This duality theorem is compatible with the $\mathbb{Z}_{2}$-Poincar\'e duality for real projective varieties with connected full real points. Indiana University Mathematics Journal 2010 text pdf 10.1512/iumj.2010.59.3790 10.1512/iumj.2010.59.3790 en Indiana Univ. Math. J. 59 (2010) 327 - 384 state-of-the-art mathematics http://iumj.org/access/