**Advances in Soviet Mathematics**

1990;
333 pp;
Hardcover

MSC: Primary 53; 55; 57; 58; 14; 33; 15; 32; 35; 05; 34; 46; 93;

**Print ISBN: 978-0-8218-4100-6
Product Code: ADVSOV/1**

List Price: $167.00

AMS Member Price: $133.60

MAA Member Price: $150.30

**Electronic ISBN: 978-1-4704-4548-5
Product Code: ADVSOV/1.E**

List Price: $167.00

AMS Member Price: $133.60

MAA Member Price: $150.30

# Theory of Singularities and its Applications

Share this page *Edited by *
*V. I. Arnol′d*

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.

# Table of Contents

## Theory of Singularities and its Applications

- Cover Cover11
- Title page iii4
- Contents v6
- Introduction vii8
- Ten problems 112
- Topology of complements to discriminants and loop spaces 920
- Cohomology of knot spaces 2334
- Nonlinear generalization of the Maslov index 7182
- Singularities of light hypersurfaces and structure of hyperbolicity sets for systems of partial differential equations 105116
- Degree of smoothness for visible contours of convex hypersurfaces 119130
- Real vanishing inflections and boundary singularities 129140
- Indices for extremal embeddings of 1-complexes 137148
- Bifurcation of flattenings and Schubert cells 145156
- Projections of generic surfaces with boundaries 157168
- Generating ideals of Lagrangian varieties 201212
- Nonisolated hypersurface singularities 211222
- Structure of uniform estimates in partial phase deformation 247258
- On the stratification and singularities of the Stokes hypersurface of one- and two-parameter families of polynomials 251262
- Euler characteristics for links of Schubert cells in the space of complete flags 273284
- Weierstrass preparation theorem for finitely smooth modules 287298
- Singularities for projections of integral manifolds with applications to control and observation problems 295306
- Back Cover Back Cover1346