h-cobordism and s-cobordism Theorems: Transfer over Semialgebraic and Nash Categories, Uniform bound and Effectiveness

Kartoue, Mady Demdah

doi:10.5802/aif.2652

Ann. inst. Fourier

2011

DOI: 10.5802/aif.2652

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h-cobordism and s-cobordism Theorems: Transfer over Semialgebraic and Nash Categories, Uniform bound and Effectiveness

Mady Demdah Kartoue¹

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Simultaneous resolution of singularities in the Nash category: finiteness and effectiveness

Demdah

2015

Rev Mat Complut

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Abstract. In this paper we present new proofs using real spectra of the finiteness theorem on Nash trivial simultaneous resolution and the finiteness theorem on Blow-Nash triviality for isolated real algebraic singularities. That is, we prove that a family of Nash sets in a Nash manifold indexed by a semialgebraic set always admits a Nash trivial simultaneous resolution after a partition of the parameter space into finitely many semialgebraic pieces and in the case of isolated singularities it admits a finite Blow-Nash trivialization. We also complement the finiteness results with recursive bounds.

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Simultaneous resolution of singularities in the Nash category: finiteness and effectiveness

Demdah

2015

Rev Mat Complut

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Regular cylindrical algebraic decomposition

Davenport

Locatelli

Sankaran

2019

J. London Math. Soc.

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We show that a strong well‐based cylindrical algebraic decomposition scriptP of a bounded semi‐algebraic set S is a regular cell decomposition, in any dimension and independently of the method by which scriptP is constructed. Being well‐based is a global condition on scriptP that holds for the output of many widely used algorithms. We also show the same for S of dimension at most 3 and scriptP a strong cylindrical algebraic decomposition that is locally boundary simply connected: this is a purely local extra condition.

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Relative homotopy groups and Serre fibrations for polynomial maps

ISHIKAWA,

NGUYEN

2024

J. Math. Soc. Japan

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h-cobordism and s-cobordism Theorems: Transfer over Semialgebraic and Nash Categories, Uniform bound and Effectiveness

Cited by 3 publications

References 3 publications

Simultaneous resolution of singularities in the Nash category: finiteness and effectiveness

Simultaneous resolution of singularities in the Nash category: finiteness and effectiveness

Regular cylindrical algebraic decomposition

Relative homotopy groups and Serre fibrations for polynomial maps

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