New Developments in Singularity Theory

By: Dirk Siersma (Editor), Charles Wall (Editor), V. Zakalyukin (Editor)

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Paperback | 30 June 2001

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Singularities arise naturally in a huge number of different areas of mathematics and science. As a consequence, singularity theory lies at the crossroads of paths that connect many of the most important areas of applications of mathematics with some of its most abstract regions.
The main goal in most problems of singularity theory is to understand the dependence of some objects of analysis, geometry, physics, or other science (functions, varieties, mappings, vector or tensor fields, differential equations, models, etc.) on parameters.
The articles collected here can be grouped under three headings. (A) Singularities of real maps; (B) Singular complex variables; and (C) Singularities of homomorphic maps.

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Non-Fiction Mathematics Geometry Algebraic Geometry Medicine Medicine in General Science Physics Calculus & Mathematical Analysis Complex Analysis Differential & Riemannian Geometry Functional Analysis & Transforms

Topology

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Published: 1st September 2009

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Preface
Classifications in Singularity Theory and Their Applications	p. 3
Applications of Flag Contact Singularities	p. 35
On Stokes Sets	p. 65
Resolutions of discriminants and topology of their complements	p. 87
Classifying Spaces of Singularities and Thom Polynomials	p. 117
Singularities and Noncommutative Geometry	p. 135
The Geometry of Families of Singular Curves	p. 159
On the preparation theorem for subanalytic functions	p. 193
Computing Hodge-theoretic invariants of singularities	p. 217
Frobenius manifolds and variance of the spectral numbers	p. 235
Monodromy and Hodge Theory of Regular Functions	p. 257
Bifurcations and topology of meromorphic germs	p. 279
Unitary reflection groups and automorphisms of simple hypersurface singularities	p. 305
Simple Singularities and Complex Reflections	p. 329
Discriminants, vector fields and singular hypersurfaces	p. 351
The theory of integral closure of ideals and modules: Applications and new developments	p. 379
Nonlinear Sections of Nonisolated Complete Intersections	p. 405
The Vanishing Topology of Non Isolated Singularities	p. 447
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New Developments in Singularity Theory

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