JournalsjemsVol. 19, No. 2pp. 507–529

Algebraicity of Nash sets and of their asymmetric cobordism

  • Riccardo Ghiloni

    Università di Trento, Povo (Trento), Italy
  • Alessandro Tancredi

    Università degli Studi di Perugia, Italy
Algebraicity of Nash sets and of their asymmetric cobordism cover

A subscription is required to access this article.

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.

Cite this article

Riccardo Ghiloni, Alessandro Tancredi, Algebraicity of Nash sets and of their asymmetric cobordism. J. Eur. Math. Soc. 19 (2017), no. 2, pp. 507–529

DOI 10.4171/JEMS/672