Hilbert's sixteenth problem
1978; Elsevier BV; Volume: 17; Issue: 1 Linguagem: Inglês
10.1016/0040-9383(78)90012-5
ISSN1879-3215
Autores Tópico(s)Homotopy and Cohomology in Algebraic Topology
ResumoIN THIS article I have tried to give a self-contained account (with complete proofs) of the few results so far discovered restricting the mutual position of the ‘ovals’ in a non-singular real plane curve of even degree. The article is based mainly on recent work of Arnol’d, Rokhlin and other Soviet mathematicians. I refer to Gudkov’s survey article[6] for history, and for a discussion of related problems. A word on prerequisites. The proofs of the results are by algebraic topology, and to follow them the reader will need a basic knowledge of homology theory, including Poincare duality and (at one point) characteristic classes. However, both the problem and the results can easily be understood by anyone who knows the definition of projective space. So I hope that non-topologists will continue reading at least to the end of 91 below, and perhaps try to give new proofs of the theorems stated there.
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