Algebraicity of Nash sets and of their asymmetric cobordism
| Autor: | Alessandro Tancredi, Riccardo Ghiloni |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
TheoryofComputation_MISCELLANEOUS
cobordism Computer Science::Computer Science and Game Theory Pure mathematics semialgebraic sets Algebraic structure General Mathematics topology of real algebraic sets 01 natural sciences Set (abstract data type) Mathematics - Algebraic Geometry ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION FOS: Mathematics Nash sets algebraic models cobordism topology of real algebraic sets semialgebraic sets Point (geometry) 0101 mathematics Algebraic number Nash sets Algebraic Geometry (math.AG) Mathematics 14P20 (Primary) 14P25 14P15 (Secondary) Algebraic set Conjecture Applied Mathematics 010102 general mathematics TheoryofComputation_GENERAL Cobordism Mathematics::Geometric Topology algebraic models If and only if |
| Zdroj: | Journal of the European Mathematical Society. 19:507-529 |
| ISSN: | 1435-9855 |
| DOI: | 10.4171/jems/672 |
| Popis: | 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. 19 pages, to appear in JEMS |
| Databáze: | OpenAIRE |
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