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On homotopy groups of real algebraic varieties and their complexifications

Let X-0 be a topological component of a nonsingular real algebraic variety and i : X --> X-C is a nonsingular projective complexification of X. In this paper, we will study the homomorphism on homotopy groups induced by the inclusion map i: X-0 --> X-C and obtain several results using rational homotopy theory and other standard tools of homotopy theory.