Hardcover ISBN:  9780821841006 
Product Code:  ADVSOV/1 
333 pp 
List Price:  $167.00 
MAA Member Price:  $150.30 
AMS Member Price:  $133.60 
Electronic ISBN:  9781470445485 
Product Code:  ADVSOV/1.E 
333 pp 
List Price:  $167.00 
MAA Member Price:  $150.30 
AMS Member Price:  $133.60 

Book DetailsAdvances in Soviet MathematicsVolume: 1; 1990MSC: Primary 53; 55; 57; 58; 14; 33; 15; 32;
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 quasiclassical 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. 
Table of Contents

Articles

V. Arnold  Ten problems

V. Vassiliev  Topology of complements to discriminants and loop spaces

V. Vassiliev  Cohomology of knot spaces

A. Givental  Nonlinear generalization of the Maslov index

B. Khesin  Singularities of light hypersurfaces and structure of hyperbolicity sets for systems of partial differential equations

I. Bogaevsky  Degree of smoothness for visible contours of convex hypersurfaces

Yu. Baryshnikov  Real vanishing inflections and boundary singularities

Yu. Baryshnikov  Indices for extremal embeddings of 1complexes

M. Kazarian  Bifurcation of flattenings and Schubert cells

V. Goryunov  Projections of generic surfaces with boundaries

V. Zakalyukin  Generating ideals of Lagrangian varieties

A. Aleksandrov  Nonisolated hypersurface singularities

V. Karpushkin  Structure of uniform estimates in partial phase deformation

V. Kostov  On the stratification and singularities of the Stokes hypersurface of one and twoparameter families of polynomials

B. Shapiro and A. Vainshtein  Euler characteristics for links of Schubert cells in the space of complete flags

V. Bakhtin  Weierstrass preparation theorem for finitely smooth modules

A. Shoshitaishvili  Singularities for projections of integral manifolds with applications to control and observation problems


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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 quasiclassical 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.

Articles

V. Arnold  Ten problems

V. Vassiliev  Topology of complements to discriminants and loop spaces

V. Vassiliev  Cohomology of knot spaces

A. Givental  Nonlinear generalization of the Maslov index

B. Khesin  Singularities of light hypersurfaces and structure of hyperbolicity sets for systems of partial differential equations

I. Bogaevsky  Degree of smoothness for visible contours of convex hypersurfaces

Yu. Baryshnikov  Real vanishing inflections and boundary singularities

Yu. Baryshnikov  Indices for extremal embeddings of 1complexes

M. Kazarian  Bifurcation of flattenings and Schubert cells

V. Goryunov  Projections of generic surfaces with boundaries

V. Zakalyukin  Generating ideals of Lagrangian varieties

A. Aleksandrov  Nonisolated hypersurface singularities

V. Karpushkin  Structure of uniform estimates in partial phase deformation

V. Kostov  On the stratification and singularities of the Stokes hypersurface of one and twoparameter families of polynomials

B. Shapiro and A. Vainshtein  Euler characteristics for links of Schubert cells in the space of complete flags

V. Bakhtin  Weierstrass preparation theorem for finitely smooth modules

A. Shoshitaishvili  Singularities for projections of integral manifolds with applications to control and observation problems