Real and complex singularities : XIII International Workshop on Real and Complex Singularities, July 27-August 8, 2014, Universidade de Sao Paulo, Sao Carlos, SP, Brazil / Ana Claudia Nabarro [and three others], editors.

Format:

Book

Conference/Event

Contributor:

Nabarro, Ana Claudia, editor.

Real Sociedad Matemática Española.

Conference Name:

International Workshop on Real and Complex Singularities (13th : 2014 : Universidade de São Paulo)

Series:

Contemporary mathematics (American Mathematical Society) ; 675.

Contemporary Mathematics, 1098-3627 ; 675

Language:

English

Subjects (All):

Singularities (Mathematics)--Congresses.

Singularities (Mathematics).

Physical Description:

1 online resource (370 pages) : illustrations.

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2016.

Summary:

This volume is a collection of papers presented at the XIII International Workshop on Real and Complex Singularities, held from July 27-August 8, 2014, in São Carlos, Brazil, in honor of María del Carmen Romero Fuster's 60th birthday. The volume contains the notes from two mini-courses taught during the workshop: on intersection homology by J.-P. Brasselet, and on non-isolated hypersurface singularities and Lê cycles by D. Massey. The remaining contributions are research articles which cover topics from the foundations of singularity theory (including classification theory and invariants) to topology of singular spaces (links of singularities and semi-algebraic sets), as well as applications to topology (cobordism and Lefschetz fibrations), dynamical systems (Morse-Bott functions) and differential geometry (affine geometry, Gauss-maps, caustics, frontals and non-Euclidean geometries).

Contents:

Cover

Title page

Contents

Preface

Carmen Romero Fuster

Hurwitz equivalence for Lefschetz fibrations and their multisections

1. Introduction

2. Multisections of Lefschetz fibrations via positive factorizations

3. Equivalence of Lefschetz fibrations with multisections

4. Lefschetz fibrations which do not arise from pencils

References

The curvature Veronese of a 3-manifold immersed in Euclidean space

2. Second fundamental form and shape operators

3. Curvature locus

4. Topological types for the curvature locus

5. Curvature veronese and principal configurations

6. Curvature veronese and convexity

7. Curvature veronese and distance squared functions

Introduction to intersection homology with and without sheaves

Introduction

1. Poincaré - Lefschetz isomorphism

2. Intersection homology

3. Sheaves

4. Characterizations of the intersection complex

5. Going to Perverse sheaves

Gauss maps and duality of sphere bundles

2. Second-Order Flat Geometry of Immersions

3. Duals of Gauss Maps

4. Singularities of a Generalized Gauss Map

5. Examples

6. Conjugate Vectors

7. Duals of Sub-bundles

Topological formulas for closed semi-algebraic sets by Euler integration

2. Euler integration and the index of a critical point

3. Some preliminary lemmas

4. The index at infinity of a polynomial of variables

5. Closed semi-algebraic sets and semi-algebraic functions

On associate families of spacelike Delaunay surfaces

2. Preliminaries

3. Spacelike helicoidal CMC surfaces

4. Singularities of associate families

Generalized distance-squared mappings of ℝⁿ⁺¹ into ℝ²ⁿ⁺¹

1. Introduction.

2. Proof of the assertion (1) of Theorem 1

3. Proof of the assertion (2) of Theorem 1

4. Proof of Theorem 2

Acknowledgements

Caustics of world hyper-sheets in the Minkowski space-time

2. The Minkowski space-time

3. World hyper-sheets in the Minkowski space-time

4. Light sheets along momentary spaces

5. Contact with lightcones

6. Graph-like wave fronts

7. Unfolded light sheets of world hyper-sheets

8. Caustics of world hyper-sheets

9. World sheets in \R³₁

On genericity of a linear deformation of an isolated singularity

2. Mixed polynomials

3. H. Levine's Theory

4. Genericity linear deformations of type ( ,…, )

5. The number of cusp points

Topological classification of simple Morse Bott functions on surfaces

2. Basic concepts

3. Construction of the invariant

4. Examples

5. Realization theorem

The link of a frontal surface singularity

2. The link of a frontal surface

3. Gauss words

4. Frontal Ruled Surfaces

Non-isolated hypersurface singularities and Lê cycles

1. Lecture 1: Topology of Hypersurfaces and the Milnor fibration

2. Lecture 2: Morse Theory, the relative polar curve, and two applications

3. Lecture 3: Proper intersection theory and Lê numbers

4. Lecture 4: Properties of Lê numbers and vanishing cycles

5. Appendix

Knots and the topology of singular surfaces in ℝ⁴

2. The link of a singular surface in \R⁴

3. Generic projections

4. -constant families

A presentation matrix associated to the discriminant of a co-rank one map-germ from ℂⁿ to ℂⁿ

2. The presentation.

3. The presentation for co-rank one map germs in ( , )

4. Applications to Singularity Theory

5. Implementation

Critical points of the Gauss map and the exponential tangent map

3. Critical points of the generalized Gauss map

4. Critical points of the exponential tangent map

Minkowski medial axes and shocks of plane curves

3. Local reconstruction of the curve from the

4. The Minkowski medial axis

5. Shocks on the Minkowski medial axis

Cobordism group of Morse functions on surfaces with boundary

3. Cobordism group of Reeb-like functions

4. Proof of the main theorem

5. Lower dimensional cobordism groups

6. Problems

Acknowledgment

Affine metric for locally strictly convex manifolds of codimension 2

2. The metric of the transversal vector field

3. The equiaffine and normal plane bundle

4. Affine distance and height functions

5. -Surfaces in hypersurfaces in affine ( +2)-space

Criteria for Morin singularities for maps into lower dimensions, and applications

2. Singular sets and Hesse matrix of corank one singularities

3. Criteria

4. Criteria for small

5. First degree bifurcation of Lefschetz singularity

Legendre curves in the unit spherical bundle over the unit sphere and evolutes

2. Legendre curves in the unit spherical bundle

3. Relationships among spherical Legendre curves, Legendre curves and framed curves

4. Evolutes of fronts in the sphere

5. Evolutes of frontals in the sphere

6. Examples

Back Cover.

Notes:

Includes bibliographical references at the end of each chapters.

Description based on print version record.

"Real Sociedad Matematica Espanola."

ISBN:

1-4704-3558-6