Homology of real algebraic varieties and morphisms to spheres

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2005

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Öztürk, Ali

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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.

Subject Keywords

Algebraic geometry.

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http://etd.lib.metu.edu.tr/upload/3/12606424/index.pdf
https://hdl.handle.net/11511/15760

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

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