Algebraicity of Nash sets and of their asymmetric cobordism

Riccardo Ghiloni; Alessandro Tancredi

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arXiv · 1611.06120

Algebraicity of Nash sets and of their asymmetric cobordism

Riccardo Ghiloni·Alessandro Tancredi

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Abstract

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.

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BibTeX RIS

Riccardo Ghiloni, Alessandro Tancredi. 2016-11-18. Algebraicity of Nash sets and of their asymmetric cobordism. https://arxiv.org/abs/1611.06120

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