Thesis (Ph. D.)--University of Chicago, Dept. Mathematics, June 2000. / Includes bibliographical references. Also available on the Internet.

abstract HOMOLOGY OF REAL ALGEBRAIC VARIETIES AND MORPHISMS TO SPHERES &uml / OZT&uml / URK, Ali Ph.D., Department of Mathematics Supervisor: Assoc. Prof. Dr. Yildiray OZAN August 2005, 24 pages Let X and Y be affine nonsingular real algebraic varieties. One of the classical problems in real algebraic geometry is whether a given C1 mapping f : X ! Y can be approximated by regular mappings in the space of C1 mappings. In this thesis, we obtain some sufficient conditions in the case when Y is the standard sphere Sn. In the second part of the thesis, we study mainly the kernel of the induced map on homology i : Hk(X,R) ! Hk(XC,R), where i : X ! XC is a nonsingular projective complexification. First, using Lefshcetz Hyperplane Section Theorem we study KHk(X H,R), where H is a hyperplane. In the remaining part, we relate KHk(X,R) to the realization of cohomology classes of XC by harmonic forms.