Homology of real algebraic varieties and morphisms to spheres

Öztürk, Ali
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.
Citation Formats
A. Öztürk, “Homology of real algebraic varieties and morphisms to spheres,” Ph.D. - Doctoral Program, Middle East Technical University, 2005.