Singularity Theory

Singularity theory draws on many other areas of mathematics and, in turn, contributes to many areas both within and outside mathematics, including 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.

Singularity theory draws on and contributes to many areas both within and outside mathematics including differential and algebraic geometry, knot theory, differential equations, bifurcation theory, Hamiltonian mechanics, optics, robotics and computer vision. This volume, containing articles from well known figures, presents an up-to-date survey of research in this area.

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.