In the past ten years there has been renewed interest in the study of the topological groups of algebraic cycles on complex projective varieties, using homotopy-theoretic techniques. The idea behind these results is that, for a complex projective variety X, the homotopy invariants of the groups of p-dimensional algebraic cycles (denoted here by L_p(X), with p ≤ dimX) carry information about the algebraic structure of X. In this context, the case X = P_C~n was particularly important. The computation of the homotopy type of L_p(P_C~n) in [16] was the starting point for the definition, due to Friedlander, of a homology theory for projective varieties called Lawson homology [7]. The Lawson homology groups of a projective variety X are a set of bigraded invariants, L_pH_k(X), defined by L_pH_k(X) = π_(k-2p)L_p(X), for all k ≥ 2p. This theory was later extended to arbitrary complex varieties by Lima-Filho [25].
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