Real and Complex Singularities

M. Manoel, M. C. Romero Fuster, C. T. C. Wall

• Publisher: Cambridge University Press
• Year: 2010
• Print ISBN: 9780521169691
• eBook ISBN: 9781139119542
• Topic: Mathematics
• Subtopic: Topology
• Index: Mathematics

The biennial meetings at São Carlos have helped create a worldwide community of experts and young researchers working on singularity theory, with a special focus on applications to a wide variety of topics in both pure and applied mathematics. The tenth meeting, celebrating the 60th birthdays of Terence Gaffney and Maria Aparecida Soares Ruas, was a special occasion attracting the best known names in the area. This volume contains contributions by the attendees, including three articles written or co-authored by Gaffney himself, and survey articles on the existence of Milnor fibrations, global classifications and graphs, pairs of foliations on surfaces, and Gaffney's work on equisingularity.

Table of contents

• Cover
• Title
• Copyright
• Contents
• Preface
• 1 On a conjecture by A. Durfee
• 2 On normal embedding of complex algebraic surfaces
• 3 Local Euler obstruction, old and new, II
• 4 Branching of periodic orbits in reversible Hamiltonian systems
• 5 Topological invariance of the index of a binary differential equation
• 6 About the existence of Milnor fibrations
• 7 Counting hypersurfaces invariant by one-dimensional complex foliations
• 8 A note on topological contact equivalence
• 9 Bi-Lipschitz equivalence, integral closure and invariants
• 10 Solutions to PDEs and stratification conditions
• 11 Real integral closure and Milnor fibrations
• 12 Surfaces around closed principal curvature lines, an inverse problem
• 13 Euler characteristics and atypical values
• 14 Answer to a question of Zariski
• 15 Projections of timelike surfaces in the de Sitter space
• 16 Spacelike submanifolds of codimension at most two in de Sitter space
• 17 The geometry of Hopf and saddle-node bifurcations for waves of Hodgkin-Huxley type
• 18 Global classifications and graphs
• 19 Real analytic Milnor fibrations and a strong Lojasiewicz inequality
• 20 An estimate of the degree of L-determinacy by the degree of A-determinacy for curve germs
• 21 Regularity of the transverse intersection of two regular stratifications
• 22 Pairs of foliations on surfaces
• 23 Bi-Lipschitz equisingularity
• 24 Gaffney’s work on equisingularity
• 25 Singularities in algebraic data acquisition