abstract
HOMOLOGY OF REAL ALGEBRAIC VARIETIES AND
MORPHISMS TO SPHERES
¨ / OZT¨ / 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.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/3/12606424/index.pdf |
| Date | 01 August 2005 |
| Creators | Ozturk, Ali |
| Contributors | Ozan, Yildiray |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | Ph.D. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for public access |
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