**Contemporary Mathematics**

Volume: 569;
2012;
202 pp;
Softcover

MSC: Primary 58; 57; 32; 14; 37;

**Print ISBN: 978-0-8218-5359-7
Product Code: CONM/569**

List Price: $79.00

AMS Member Price: $63.20

MAA Member Price: $71.10

**Electronic ISBN: 978-0-8218-8780-6
Product Code: CONM/569.E**

List Price: $74.00

AMS Member Price: $59.20

MAA Member Price: $66.60

# Real and Complex Singularities

Share this page *Edited by *
*Victor Goryunov; Kevin Houston; Roberta Wik-Atique*

This volume is a collection of papers presented at the 11th International Workshop on Real and Complex Singularities, held July 26–30, 2010, in São Carlos, Brazil, in honor of David Mond's 60th birthday. This volume reflects the high level of the conference discussing the most recent results and applications of singularity theory. Articles in the first part cover pure singularity theory: invariants, classification theory, and Milnor fibres. Articles in the second part cover singularities in topology and differential geometry, as well as algebraic geometry and bifurcation theory: Artin-Greenberg function of a plane curve singularity, metric theory of singularities, symplectic singularities, cobordisms of fold maps, Goursat distributions, sections of analytic varieties, Vassiliev invariants, projections of hypersurfaces, and linearity of the Jacobian ideal.

#### Readership

Graduate students and research mathematicians interested in singularities in geometry and topology.

# Table of Contents

## Real and Complex Singularities

- Preface ix10 free
- David Mond xi12 free
- Milnor Fibrations and the Concept of 𝑑-regularity for Analytic Map Germs 116 free
- Bi-Lipschitz 𝒢-triviality and Newton polyhedra, 𝒢=ℛ, 𝒞, 𝒦, ℛ_{𝒱}, 𝒞_{𝒱}, 𝒦_{𝒱} 2944
- Symplectic 𝑆_{𝜇} Singularities 4560
- Topology of the real Milnor fiber for isolated singularities 6782
- Compact 3-manifolds supporting some ℝ²-actions 7792
- Timelike canal hypersurfaces of spacelike submanifolds in a de Sitter space 87102
- 1. Introduction 87102
- 2. Timelike hypersurfaces in a de Sitter space 88103
- 3. Spacelike submanifolds in the de Sitter space 91106
- 4. Timelike canal hypersurfaces 92107
- 5. De Sitter 𝜃-maps as wavefronts 95110
- 6. Contact with hyperbolic hyperquadrics in the de Sitter space 97112
- 7. Generic properties of spacelike submanifolds 99114
- References 100115

- Residues in K-theory 101116
- Multicusps 115130
- Small growth vectors of the compactifications of the contact systems on 𝐽^{𝑟}(1,1) 123138
- Vassiliev type invariants for generic mappings, revisited 143158
- Sections of Analytic Variety 161176
- The Artin-Greenberg function of a plane curve singularity 177192
- 1. Introduction 177192
- 2. Characteristic sequences and semigroup of a reducible polynomial 178193
- The tree of contacts of Abhyankar-Assi 179194
- 3. The Artin-Greenberg function 181196
- 4. The Artin-Greenberg function for a reducible polynomial with two branches 183198
- 5. The Artin-Greenberg function of a reducible polynomial with many branches 189204
- References 191206

- Singularities with critical locus a complete intersection and transversal type 𝐴₁ 193208