Singularities of Mappings

DOI10.1007/978-3-030-34440-5zbMath1448.58032OpenAlexW4247579952MaRDI QIDQ5208017

Juan Jose Nuño-Ballesteros, D. M. Q. Mond

Publication date: 14 January 2020

Published in: Grundlehren der mathematischen Wissenschaften (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-34440-5

zbMATH Keywords

stabilitycomplete intersectionsdualitycanonical moduletopological stabilityright-left equivalenceknot theorydiscriminantsGorenstein ringsmaximal Cohen-Macaulay modulesfinite determinacyReidemeister movesrank conditionFitting idealscritical spacestable perturbationscontact equivalencetriple pointsbifurcation setssingularities of mappingsThom-Boardman singularitiesversal unfoldingsconductor idealsThom-Mather theorymultiple point spacesunipotent algebraic groupsnice dimensionsdiscriminant Milnor numbersdisentanglement of a mapfree and almost free divisorsimage Milnor numbersisosingular locuslocal conical structurelogarithmic tangent spacelogarithmic transversalityparameterised hypersurfacesunstable map-germsvector fields and flows

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Complex surface and hypersurface singularities (32S25) Research exposition (monographs, survey articles) pertaining to global analysis (58-02) Milnor fibration; relations with knot theory (32S55) Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) (32S60) Symmetries, equivariance on manifolds (58K70) Local complex singularities (32S05) Critical points of functions and mappings on manifolds (58K05) Topological properties of mappings on manifolds (58K15) Classification; finite determinacy of map germs (58K40) Deformation of singularities (58K60) Stability theory for manifolds (58K25) Knot theory (57K10)

Related Items (22)

Old and New Results on Density of Stable Mappings ⋮ Singularities of Mappings ⋮ Characteristic Classes ⋮ Double points in families of map germs from ℝ2 to ℝ3 ⋮ Liftable vector fields, unfoldings and augmentations ⋮ Singularities of mappings on ICIS and applications to Whitney equisingularity ⋮ On Betti numbers of the gluing of germs of formal complex spaces ⋮ Curvature loci of 3‐manifolds ⋮ Thom condition and monodromy ⋮ The dual tree of a fold map germ from to ⋮ Singularities of 3-parameter line congruences in ⋮ Simplicity of augmentations of codimension 1 germs and by Morse functions ⋮ Iterated multiple points I: Equations and pathologies ⋮ Topology of fold map germs from \(\mathbb{R}^3\) to \(\mathbb{R}^5\) ⋮ On k-folding map-germs and hidden symmetries of surfaces in the Euclidean 3-space ⋮ Cross-caps, triple points and a linking invariant for finitely determined germs ⋮ On the topology of the transversal slice of a quasi-homogeneous map germ ⋮ Singularities of frontal surfaces ⋮ Reflection maps ⋮ Image Milnor number formulas for weighted-homogeneous map-germs ⋮ The extra-nice dimensions ⋮ Families of ICIS with constant total Milnor number

Uses Software

• Macaulay2
• Mathematica
• SINGULAR
• Transversal

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