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Geometric properties of generic differentiable manifolds

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Oscillatory integrals, lagrange immersions and unfolding of singularities
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Tangents to an Analytic Variety
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Geometric Invariant Theory
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Geometric Invariant Theory
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Counterexamples in Stratification Theory: Two Discordant Horns
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Characteristic class entering in quantization conditions
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Normal forms for functions near degenerate critical points, the Weyl groups of Ak, Dk, Ek and Lagrangian singularities
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Stratifications de Whitney et théorème de Bertini-Sard
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Relations between a manifold and its focal set
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Generic properties of geodesic flows
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Riemannsche Flächen im ebenen Raum von vier Dimensionen
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Fourier integral operators. I
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Fourier integral operators. II
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On singularities of submanifolds of higher dimensional Euclidean spaces
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Quelques propriétés globales des variétés différentiables
inferredcites →https://doi.org/10.1007/bf02684653openalex-snapshot
Un théorème des fonctions implicites pour les espaces d’applications C ∞
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La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie
inferredcites →https://doi.org/10.1007/bf02684889openalex-snapshot
Stability of C ∞ mappings, IV. Classification of stable germs by R -algebras
inferredcites →https://doi.org/10.1007/bf02698926openalex-snapshot
Stability of C ∞ mappings, III. Finitely determined map-germs
inferredcites →https://doi.org/10.1007/bfb0057305openalex-snapshot
Travaux de thom et mather sur la stabilité topologique
inferredcites →https://doi.org/10.1007/bfb0061658openalex-snapshot
Stability of Unfoldings
inferredcites →https://doi.org/10.1007/bfb0068899openalex-snapshot
Geometric differentiation — A thomist view of differential geometry
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Topological Stability of Smooth Mappings
inferredcites →https://doi.org/10.1016/0001-8708(70)90028-9openalex-snapshot
Stability of C∞ mappings: V, transversality
inferredcites →https://doi.org/10.1016/0001-8708(71)90020-xopenalex-snapshot
Symplectic manifolds and their lagrangian submanifolds
inferredcites →https://doi.org/10.1016/0040-9383(62)90103-9openalex-snapshot
Differential geometry of higher order
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Morse theory on Hilbert manifolds
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On differentiable functions with isolated critical points
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The focal set of a hypersurface with Abelian fundamental group
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Stabilité structurelle et morphogenèse
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The singularities of C∞-functions of right-codimension smaller or equal than eight
inferredcites →https://doi.org/10.1016/b978-0-12-550350-1.50021-7openalex-snapshot
Stratifications and Mappings††AMS (MOS) 1970 SUBJECT CLASSIFICATION: 58C25.‡‡This Chapter is based on lectures I gave at the Dynamical Systems conference. I wrote up these lectures partly during a stay at IMPA. I have developed these ideas over a period of years at Princeton, IHES, Harvard, and…
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Methods of Algebraic Geometry
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Methods of Algebraic Geometry. By W. V. D. Hodge and D. Pedoe. Vol. I: pp. viii, 440; Vol. II: pp. ix, 394. Paperback edition. 17s. 6d. each volume. (Cambridge.)
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LOCAL TOPOLOGICAL PROPERTIES OF DIFFERENTIABLE MAPPINGS
inferredcites →https://doi.org/10.1070/rm1974v029n02abeh003846openalex-snapshot
NORMAL FORMS OF FUNCTIONS IN NEIGHBOURHOODS OF DEGENERATE CRITICAL POINTS
inferredcites →https://doi.org/10.1073/pnas.21.4.225openalex-snapshot
Connections between Differential Geometry and Topology
inferredcites →https://doi.org/10.1090/pspum/015/0264713openalex-snapshot
Transversal approximation on Banach manifolds
inferredcites →https://doi.org/10.1090/pspum/015/0271993openalex-snapshot
The generic conjugate locus
inferredcites →https://doi.org/10.1090/s0002-9904-1963-10969-6openalex-snapshot
Transversality in manifolds of mappings
inferredcites →https://doi.org/10.1090/s0002-9904-1969-12138-5openalex-snapshot
Ensembles et morphismes stratifiés
inferredcites →https://doi.org/10.1090/s0002-9904-1976-14107-9openalex-snapshot
Deformations of geodesic fields
inferredcites →https://doi.org/10.1090/s0002-9904-1976-14125-0openalex-snapshot
The existence of nontriangulable cut loci
inferredcites →https://doi.org/10.1090/s0002-9947-1965-0185602-6openalex-snapshot
The geometry of immersions. I
inferredcites →https://doi.org/10.1093/qmath/os-17.1.1openalex-snapshot
THE FIVE-DIMENSIONAL GEOMETRY OF THE CURVATURE TENSOR IN A RIEMAININIAN V4
inferredcites →https://doi.org/10.1098/rstl.1863.0010openalex-snapshot
X. On the distribution of surfaces of the third order into species, in reference to the absence or presence of singular points, and the reality of their lines
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VII. A memoir on cubic surfaces
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Foundations Of Mechanics
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Connections between differential geometry and topology. I. Simply connected surfaces
inferredcites →https://doi.org/10.1515/9781400883905openalex-snapshot
The Classical Groups
inferredcites →https://doi.org/10.1515/9781400884087-013openalex-snapshot
11. The Imbedding Problem for Riemannian Manifolds
inferredcites →https://doi.org/10.2307/1968482openalex-snapshot
Differentiable Manifolds
inferredcites →https://doi.org/10.2307/1969989openalex-snapshot
The Imbedding Problem for Riemannian Manifolds
inferredcites →https://doi.org/10.2307/1970246openalex-snapshot
Images of Critical Sets
inferredcites →https://doi.org/10.2307/1970400openalex-snapshot
Tangents to an Analytic Variety
inferredcites →https://doi.org/10.2307/1970595openalex-snapshot
Stability of C ∞ Mappings: I. The Division Theorem
inferredcites →https://doi.org/10.2307/1970668openalex-snapshot
Stability of C ∞ Mappings: II. Infinitesimal Stability Implies Stability
inferredcites →https://doi.org/10.2307/1970783openalex-snapshot
Generic Projections
inferredcites →https://doi.org/10.2307/1970796openalex-snapshot
Implicit Function Theorems and Isometric Embeddings
inferredcites →https://doi.org/10.2307/20025687openalex-snapshot
Differential Geometry of Two Dimensional Surfaces in Hyperspace
inferredcites →https://doi.org/10.2307/2373064openalex-snapshot
The Conjugate Locus of a Riemannian Manifold
inferredcites →https://doi.org/10.24033/asens.1274openalex-snapshot
Intégrales asymptotiques et monodromie
inferredcites →https://doi.org/10.4310/jdg/1214430015openalex-snapshot
The normal singularities of a submanifold
inferredcites →https://doi.org/10.4310/jdg/1214430644openalex-snapshot
Sur le cut-locus d'une variété plongée
inferredcites →https://doi.org/10.4310/jdg/1214433166openalex-snapshot
Natural tensors on Riemannian manifolds
inferredcites →https://doi.org/10.4310/jdg/1214433427openalex-snapshot
Existence of infinitely many closed geodesics
inferredcites →https://doi.org/10.5802/aif.340openalex-snapshot
Sur les singularités des formes différentielles
inferredcites →https://doi.org/10.5802/aif.455openalex-snapshot
Catastrophes and partial differential equations

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Geometrical Characterizations of Singularities of the Gauss Map on Generically Immersed 3-Manifolds in R4
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On Computing Aspect Graphs of Smooth Shapes from Volumetric Data
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Computing exact aspect graphs of curved objects: Algebraic surfaces
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Shade, Shadow and Shape
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Singularities of Lagrangian varieties and related topics
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Caustics by reflexion in the extended plane
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Bifurcations of the center of symmetry
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Generic singularities of the exponential map on Riemannian manifolds
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Existenz eines 6-Normalenpunktes in einem konvexen K�rper
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Stability of transversality to a stratification implies Whitney (a)-regularity
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Punctual Hilbert schemes and resolutions of multiple point singularities
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On parametric nonlinear programming
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Pappus type theorems for hypersurfaces in a space form
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Caustics through the looking glass
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Seeing—the mathematical viewpoint
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Generic embeddings, Gauss maps and stratipications
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Bifurcation from a manifold
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Symmetric lagrangian singularities and Gauss maps of theta divisors
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Some global properties of closed space curves
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Fold Gauss Maps and their Weighted Graphs
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Geometrical characterizations of singularities of the Gauss map on generically immersed 3-manifolds in $${\mathbb {R}}^4$$
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Hamilton--Jacobi Equations and Distance Functions on Riemannian Manifolds
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Stable Gauss maps from a global viewpoint
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Generic Geometry of Stable Maps of 3-Manifolds into $${\mathbb {R}}^4$$
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On singularities of the Galilean spherical darboux ruled surface of a space curve in G 3
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Singularities and dualities of evolving developable frontals
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The medial axis of any closed bounded set is locally Lipschitz stable with respect to the Hausdorff distance under ambient diffeomorphisms
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Burning or Collapsing the Medial Axis is Unstable
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Classification of linear connections
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Stability criteria and classification of singularities for equivariant lagrangian submanifolds
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On caustics by reflexion
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Closed curves with no quadrisecants
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On the classification of views of piecewise smooth objects
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A shape representation for computer vision based on differential topology
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Singularities of flat extensions from generic surfaces with boundaries
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Invariants and quasi-umbilicity of timelike surfaces in Minkowski space R3,1
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A finite dimensional approach to light rays in General Relativity
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Geometric invariants of surfaces in R4
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Hamiltonian geodesics in nonholonomic differential systems
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Conic lagrangian singularities
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Isotropic varieties in the singular symplectic geometry
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Focal Sets in Certain Riemannian Manifolds
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On generic hypersurfaces in ℝn
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The parallel rank of a submanifold of Euclidean space
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Generalized Luneburg canonical varieties and vector fields on quasicaustics
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Generic Geometry
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ON SOME OPERATIONS PRESERVING GENERIC PROPERTIES OF SYSTEMS
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Caustics and Diffraction from a Line Source
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An Elementary Approach to Generic Properties of Plane Curves
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On Legendrian Singularities
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Parallel Translation of Curvature Along Geodesics
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On the Heat Diffusion for Generic Riemannian and Sub-Riemannian Structures
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PROJECTIONS OF SPACE CURVES AND DUALITY
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Source genericity of caustics by reflexion in R3
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Positive feedback interconnection of Hamiltonian systems
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On computing aspect graphs of smooth shapes from volumetric data
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Computing exact aspect graphs of curved objects: solids of revolution
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On Generic Composites of Maps
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Projection genericity of space curves
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The Convex Hull of a Hypersurface
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Caustics in Extended Euclidean Space
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QUADRISECANTS OF KNOTS AND LINKS
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Heterogeneous Riemannian Manifolds
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"Geometria das singularidades de projeções"
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Flat and Round Singularity theory
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Geometria local associada à aplicação de Gauss de hipersuperfícies em R>sup<4>/sup<
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Stability of geodesics in the Brownian map
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Local topological models of envelopes
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Projection of generic 1 and 2-parameter families of space curves
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Tangent varieties and openings of map-germs
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Focal stability of Riemann metrics
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Port-Hamiltonian Systems Theory: An Introductory Overview
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A metric property of umbilic points
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Cut Loci and Distance Functions
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Combinatorial cohomology of the space of long knots
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On isotropic submanifolds and evolution of quasicaustics
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Scattering of Geodesic Fields, I
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Isolated roundings and flattenings of submanifolds in Euclidean spaces
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Some Considerations on the Cut Locus of a Riemannian Manifold
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Surfaces in 3-space and their contact with circles
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Lines and circles joining components of a link
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Hamiltonian Boundary Value Problems, Conformal Symplectic Symmetries, and Conjugate Loci
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Singularities of Tangent Varieties to Curves and Surfaces
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