Stratification Theory

DOI10.1007/978-3-030-53061-7_4zbMath1478.32001OpenAlexW4210992244MaRDI QIDQ5014454

David J. A. Trotman

Publication date: 2 December 2021

Published in: Handbook of Geometry and Topology of Singularities I (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-53061-7_4

zbMATH Keywords

\(C^\infty\) stratified setsstratifications of definable setsstratifications of subanalytic sets

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces (32-02) (C^infty)-functions, quasi-analytic functions (26E10) Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) (32S60) Semi-analytic sets, subanalytic sets, and generalizations (32B20) Research exposition (monographs, survey articles) pertaining to real functions (26-02)

Related Items (4)

On rational convexity of totally real sets ⋮ On structural stability of evolutionary stable strategies ⋮ Algebro-Geometric Equisingularity of Zariski ⋮ Introduction to Mixed Hypersurface Singularity

Cites Work

• Weak Whitney regularity implies equimultiplicity for families of complex hypersurfaces
• Euler flag enumeration of Whitney stratified spaces
• A geometric proof of the existence of definable Whitney stratifications
• Local structures on stratified spaces
• Arc-wise analytic stratification, Whitney fibering conjecture and Zariski equisingularity
• Definable triangulations with regularity conditions
• Local features in natural images via singularity theory
• Detecting Thom faults in stratified mappings
• Elementary structure of real algebraic varieties
• Stratified mappings - structure and triangulability
• Theorème de De Rham pour les variétés stratifiées. (The De Rham theorem for stratified manifolds)
• Lipschitz triangulations
• Vector fields on singular varieties
• Abstract prestratified sets are (b)-regular
• Transverse transversals and homeomorphic transversals
• Conditions de régularité et éclatements. (Regularity conditions and blowing-ups)
• Volume on stratified sets
• On (\(\omega\) ) and \((t^ s)\)-regular stratifications
• Densité des ensembles sous-analytiques. (On the density of subanalytic sets)
• Une version microlocale de la condition (w) de Verdier. (A microlocal version of the condition (w) of Verdier)
• Verdier and strict Thom stratifications in o-minimal structures
• La stabilité topologique des applications polynomiales
• Sufficiency of jets via stratification theory
• Whitney regularity and generic wings
• Intersection homology theory
• The realization of abstract stratified sets
• Integral closure of modules and Whitney equisingularity
• Stratification of real analytic mappings and images
• Triangulation of subanalytic sets and proper subanalytic maps
• Stratifications de Whitney et théorème de Bertini-Sard
• Types topologiques des polynômes
• On Thom-Whitney stratification theory
• Topological stability of smooth mappings
• Stability of transversality to a stratification implies Whitney (a)- regularity
• Whitney homology, cohomology and Steenrod squares
• On stratified Morse theory
• Limits of tangent spaces to fibres and the \(w_ f\) condition
• Geometry of subanalytic and semialgebraic sets
• The Kuo condition, an inequality of Thom's type and \((c)\)-regularity
• On metric properties of stratified sets
• Whitney, Kuo-Verdier and Lipschitz stratifications for the surfaces \(y^{a}=z^{b}x^{c}+x^{d}\)
• A stratified homotopy hypothesis
• Variation of the Green function on Riemann surfaces and Whitney's holomorphic stratification conjecture
• Thom's conjecture on triangulations of maps
• Scribbling continua in \(\mathbb{R}^ n\) and constructing singularities with prescribed Nash fibre and tangent cone
• Champs totalement radiaux sur une structure de Thom-Mather. (Totally radial vector fields on a Thom-Mather space.)
• Geometric categories and o-minimal structures
• Lipschitz stratifications in power-bounded \(o\)-minimal fields
• A bilipschitz version of Hardt's theorem
• Real Milnor fibrations and \((C)\)-regularity
• Tangents to an analytic variety
• Normal cones in analytic Whitney stratifications
• Characterizations of v-sufficiency of jets
• Équisingularité réelle : nombres de Lelong et images polaires
• Stratification Theory from the Weighted Point of View
• Lipschitz stratifications in o-minimal structures
• The signature package on Witt spaces
• On the stratification by orbit types
• Triangulations of non-proper semialgebraic Thom maps
• Cône normal et régularités de Kuo-Verdier
• Equisingularity of sections, (𝑡^{𝑟}) condition, and the integral closure of modules
• On Proving the Geometric Versions of Whitney Regularity
• Sur la condition de Thom stricte pour un morphisme analytique complexe
• Blowing-Up and Whitney (a)-Regularity
• Whitney (b)-regularity is weaker than Kuo's ratio test for real algebraic stratifications.
• Geometric versions of Whitney regularity for smooth stratifications
• Whitney $(a)$-faults which are hard to detect
• Semi-Algebraic Local-Triviality in Semi-Algebraic Mappings
• Whitney Stratified Chains and Cochains
• A Transversality Property Weaker than Whitney (A)-Regularity
• The Invariance of Milnor's Number Implies the Invariance of the Topological Type
• Differential Topology
• Triangulation of Stratified Objects
• Exponentiation is Hard to Avoid
• Lipschitz stratification of subanalytic sets
• LIPSCHITZ STRATIFICATIONS AND GENERIC WINGS
• Stratifications and Finite Determinacy
• Local polar varieties in the geometric study of singularities
• Corrigendum: Briançon-Speder examples and the failure of weak Whitney regularity
• Whitney stratifications and the continuity of local Lipschitz–Killing curvatures
• On the local geometry of definably stratified sets
• Notes on Topological Stability
• Transversal homotopy theory
• Stratified Submersions and Condition (D)
• Medial/Skeletal Linking Structures for Multi-Region Configurations
• STRATIFIED TRANSVERSALITY OF HOLOMORPHIC MAPS
• Poincaré-Hopf theorems on singular spaces
• Volume, Whitney conditions and Lelong number
• Whitney triangulations of semialgebraic sets
• Briançon-Speder examples and the failure of weak Whitney regularity
• The Geometry of Immersions. I
• Ensembles et morphismes stratifiés
• Some open questions in the theory of singularities
• Differential Topology
• An invitation to Morse theory
• Analytic and geometric study of stratified spaces
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