Overview

Singularity theory is a broad subject with vague boundaries. It draws on many other areas of mathematics, and in turn has contributed to many areas both within and outside mathematics, in particular differential and algebraic geometry, knot theory, differential equations, bifurcation theory, Hamiltonian mechanics, optics, robotics and computer vision. This volume consists of two dozen articles from some of the best known figures in singularity theory, and it presents an up-to-date survey of research in this area.

Full Product Details

Author:   W. Bruce (University of Liverpool) ,  D. Mond (University of Warwick)
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press (Virtual Publishing)
Volume:   263
ISBN:  

9780511569265

ISBN 10:   0511569262
Publication Date:   05 May 2013
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Undefined
Publisher's Status:   Active
Availability:   Available To Order  
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Table of Contents

Part I. Complex Singularities: 1. Singularities arising from lattice polytopes K. Altmann; 2. Critical points of affine multiforms on the complement of arrangements J. N. Damon; 3. Strange duality, mirror symmetry and the Leech lattice W. Ebeling; 4. Geometry of equisingular families of curves G.-M. Greuel and E. Shustin; 5. Arrangements, KZ systems and Lie algebra homology E. J. N. Looijenga; 6. The signature of f(x,y) +zN A. Nemethi; 7. Spectra of K-unimodal isolated singularities of complete intersections J. M. Steenbrink; 8. Dynkin graphs, Gabrielov graphs and triangle singularities T. Urabe; Part II. Stratifications and Equisingularity Theory: 9. Differential forms on singular varieties and cyclic homology J. P. Brasselet and Y. Legrand; 10. Continuous controlled vector fields A. A. du Plessis; 11. Finiteness of Mather's canonical stratification A. A. du Plessis; 12. Trends in equisingularity theory T. J. Gaffney and D. Massey; 13. Regularity at infinity of real and complex polynomial maps M. Tibar; Part III. Global Singularity Theory: 14. A Bennequin number estimate for transverse knots V. V. Goryunov and J. W. Hill; 15. Abelian covers of the projective plane A. Libgober; 16. Elimination of singularities: Thom polynomials and beyond O. Saeki and K. Sukuma; Part IV. Singularities of Mappings: 17. An introduction to the image-computing spectral sequence K. A. Houston; 18. On the classification and geometry of Corank 1 map-germs from 3-space to 4-space K. A. Houston and N. P. Kirk; 19. Multiplicities of zero-schemes in quasi-homogeneous Corank-1 singularities W. L. Marar, J. A. Montaldi and M. A. S. Ruas; 20. Butterflies and umbilics of stable perturbations of analytic map-germs C5,0 → C4,0 T. Fukui; Part V. Applications of Singularity Theory: 21. Singular phenomena in kinematics P. S. Donelan and C. G. Gibson; 22. Singularities of developable surfaces G. Ishikawa; 23. Singularities of solutions for first order partial differential equations S. Izumiya.

Reviews

' … presents an up-to-date survey of research in this area.' Extrait de L'Enseignement Mathématique

' ... presents an up-to-date survey of research in this area.' Extrait de L'Enseignement Mathematique

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