Algebraicity of Nash sets and of their asymmetric cobordism

作者：Ghiloni Riccardo^*; Tancredi Alessandro

来源：Journal of the European Mathematical Society, 2017, 19(2): 507-529.

DOI：10.4171/JEMS/672

• Nash sets
• algebraic models
• cobordism
• topology of real algebraic sets
• semialgebraic sets

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.

• 出版日期2017
• 单位Perugia