Theory of Singularities and Its Applications

Covers such topics as construction of new knot invariants, stable cohomology of complementary spaces to diffusion diagrams, topological properties of spaces of Legendre maps, application of Weierstrass bifurcation points in projective curve flattenings, classification of singularities of projective surfaces with boundary, and control theory.

The theory of singularities lies at the crossroads between those branches of mathematics which are the most abstract and those which are the most applied. Algebraic and differential geometry and topology, commutative algebra and group theory are as intimately connected to singularity theory as are dynamical systems theory, control theory, differential equations, quantum mechanical and quasi-classical asymptotics, optics, and functional analysis. This collection of papers incorporates recent results of participants in the editor''s ongoing seminar in singularity theory, held in the Mechanics and Mathematics Department of Moscow University for over twenty years. With its broad range of subject matter, this volume will appeal to a wide range of readers in various areas of the mathematical sciences.Among the topics covered are: construction of new knot invariants, stable cohomology of complementary spaces to diffusion diagrams, topological properties of spaces of Legendre maps, application of Weierstrass bifurcation points in projective curve flattenings, classification of singularities of projective surfaces with boundary, nonsmoothness of visible contours of smooth convex hypersurfaces, flag manifolds, hyperbolic partial differential systems, and control theory.