eBook ISBN:  9781470446192 
Product Code:  ADVSOV/21.E 
List Price:  $136.00 
MAA Member Price:  $122.40 
AMS Member Price:  $108.80 
eBook ISBN:  9781470446192 
Product Code:  ADVSOV/21.E 
List Price:  $136.00 
MAA Member Price:  $122.40 
AMS Member Price:  $108.80 

Book DetailsAdvances in Soviet MathematicsVolume: 21; 1994; 262 ppMSC: Primary 57; 58; Secondary 14
This book contains papers growing out of recent work of the Singularity Seminar at Moscow State University. The main topic of most of the papers is the analysis of singularities of discriminant hypersurfaces formed by the degenerate objects in different spaces of mappings. Among the topics covered are: the space of mappings of the circle to threespace; invariants, bifurcations, and classifications of plane curves; algebraic invariants of the Morse complex; complex boundary singularities; spaces of morsifications of singularities; and the number of singular points on a complex projective hypersurface.
ReadershipUndergraduate students in mathematics, active researchers, physicists specializing in quantum field theory.

Table of Contents

Articles

F. Aicardi — Treelike curves

V. I. Arnold — Plane curves, their invariants, Perestroikas, and classifications

S. A. Barannikov — The framed Morse complex and its invariants

S. V. Chmutov, S. V. Duzhin and S. K. Lando — Vassiliev knot invariants. I: Introduction

S. V. Chmutov, S. V. Duzhin and S. K. Lando — Vassiliev Knot invariants. II: Intersection graph conjecture for trees

S. V. Chmutov, S. V. Duzhin and S. K. Lando — Vassiliev knot invariants. III: Forest algebra and weighted graphs

Victor V. Goryunov — Symmetric quartics with many nodes

Victor V. Goryunov — Subprincipal Springer cones and Morsifications of Laurent polynomials and $D_{\mu }$ singularities

S. M. GuseinZade — On the enumeration of curves from infinity to infinity

Alexander B. Merkov — On the classification of ornaments

I. Shcherbak and A. Szpirglas — Boundary singularities: Topology and duality

Victor A. Vassiliev — Invariants of ornaments


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This book contains papers growing out of recent work of the Singularity Seminar at Moscow State University. The main topic of most of the papers is the analysis of singularities of discriminant hypersurfaces formed by the degenerate objects in different spaces of mappings. Among the topics covered are: the space of mappings of the circle to threespace; invariants, bifurcations, and classifications of plane curves; algebraic invariants of the Morse complex; complex boundary singularities; spaces of morsifications of singularities; and the number of singular points on a complex projective hypersurface.
Undergraduate students in mathematics, active researchers, physicists specializing in quantum field theory.

Articles

F. Aicardi — Treelike curves

V. I. Arnold — Plane curves, their invariants, Perestroikas, and classifications

S. A. Barannikov — The framed Morse complex and its invariants

S. V. Chmutov, S. V. Duzhin and S. K. Lando — Vassiliev knot invariants. I: Introduction

S. V. Chmutov, S. V. Duzhin and S. K. Lando — Vassiliev Knot invariants. II: Intersection graph conjecture for trees

S. V. Chmutov, S. V. Duzhin and S. K. Lando — Vassiliev knot invariants. III: Forest algebra and weighted graphs

Victor V. Goryunov — Symmetric quartics with many nodes

Victor V. Goryunov — Subprincipal Springer cones and Morsifications of Laurent polynomials and $D_{\mu }$ singularities

S. M. GuseinZade — On the enumeration of curves from infinity to infinity

Alexander B. Merkov — On the classification of ornaments

I. Shcherbak and A. Szpirglas — Boundary singularities: Topology and duality

Victor A. Vassiliev — Invariants of ornaments