Geodesic
Algebraicity of Nash sets and of their asymmetric cobordism
Journal of the European Mathematical Society, Tome 19 (2017) no. 2, pp. 507-529

Voir la notice de l'article provenant de la source EMS Press

This paper deals with the existence of algebraic structures on compact Nash sets. We introduce the algebraic-topological notion of asymmetric Nash cobordism between compact Nash sets, and we prove that a compact Nash set is semialgebraically homeomorphic to a real algebraic set if and only if it is asymmetric Nash cobordant to a point or, equivalently, if it is strongly asymmetric Nash cobordant to a real algebraic set. As a consequence, we obtain new large classes of compact Nash sets semialgebraically homeomorphic to real algebraic sets. To prove our results, we need to develop new algebraic-topological approximation procedures. We conjecture that every compact Nash set is asymmetric Nash cobordant to a point, and hence semialgebraically homeomorphic to a real algebraic set.
DOI : 10.4171/jems/672
Classification : 14-XX
Keywords: Nash sets, algebraic models, cobordism, topology of real algebraic sets, semialgebraic sets 
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     title = {Algebraicity of {Nash} sets and of their asymmetric cobordism},
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Riccardo Ghiloni; Alessandro Tancredi. Algebraicity of Nash sets and of their asymmetric cobordism. Journal of the European Mathematical Society, Tome 19 (2017) no. 2, pp. 507-529. doi: 10.4171/jems/672

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