Finite determinacy and topological triviality. I

DOI10.1007/BF01389162zbMath0489.58003OpenAlexW2022524602MaRDI QIDQ1166809

James Damon

Publication date: 1980

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142774

zbMATH Keywords

construction of topologically versal germstopological triviality in deformationstopological triviality of unfoldingsweighted homogeneous polynomial germs

Mathematics Subject Classification ID

Deformations of complex singularities; vanishing cycles (32S30) Theory of singularities and catastrophe theory (58K99) Differentiable maps on manifolds (58C25)

Related Items (26)

On right-equivalence ⋮ Weighted homogeneous maps from the plane to the plane ⋮ Old and New Results on Density of Stable Mappings ⋮ Double points in families of map germs from ℝ2 to ℝ3 ⋮ Versal topological stratification and the bifurcation geometry of map-germs of the plane ⋮ The link of a finitely determined map germ from \(R^{2}\) to \(R^{2}\) ⋮ Finite determinacy of matrices and ideals ⋮ The versality discriminant and local topological equivalence of mappings ⋮ Topological sufficiency of smooth map-germs ⋮ Finite determinacy and topological triviality. I ⋮ Bi-Lipschitz \(\mathcal A\)-triviality of map germs and Newton filtrations ⋮ \(\mathcal A\)-codimension and the vanishing topology of discriminants ⋮ Unnamed Item ⋮ Completions, branched covers, Artin groups, and singularity theory ⋮ On finite determinacy for matrices of power series ⋮ The doodle of a finitely determined map germ from \(\mathbb R^2\) to \(\mathbb R^3\) ⋮ Topological equivalence of germs of functions ⋮ Finitely determined singularities of ruled surfaces in ³ ⋮ The duals of generic space curves and complete intersections ⋮ Topological Triviality of a Family of Zero-Sets ⋮ Topological triviality of versal unfoldings of complete intersections ⋮ Topological triviality of deformations of functions and Newton filtrations ⋮ The Topology of the Milnor Fibration ⋮ Universal topological stratification for the Pham example ⋮ Mapping fibrations ⋮ Pre-weighted homogeneous map germs—Finite determinacy and topological triviality

Cites Work

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• Topological stability in the nice dimensions
• Finite determinacy and topological triviality. I
• On the order of determination of a finitely determined germ
• On the semi-universal deformation of a simple-elliptic hypersurface singularity. I: Unimodularity
• Stability of \(C^\infty\) mappings. II: Infinitesimal stability implies stability
• The Invariance of Milnor's Number Implies the Invariance of the Topological Type
• The Invariance of Milnor's Number Implies Topological Triviality

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