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Singularities and Bifurcations
Edited by: V. I. Arnold

Advances in Soviet Mathematics
1994; 262 pp; hardcover
Volume: 21
ISBN-10: 0-8218-0237-2
ISBN-13: 978-0-8218-0237-3
List Price: US$122
Member Price: US$97.60
Order Code: ADVSOV/21
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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 three-space; 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.

Table of Contents

  • F. Aicardi -- Tree-like 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
  • V. V. Goryunov -- Symmetric quartics with many nodes
  • V. V. Goryunov -- Subprincipal Springer cones and morsifications of Laurent polynomials and \(D_\mu\) singularities
  • S. M. Gusein-Zade -- On the enumeration of curves from infinity to infinity
  • A. B. Merkov -- On the classification of ornaments
  • I. Shcherbak and A. Szpirglas -- Boundary singularities: Topology and duality
  • V. A. Vassiliev -- Invariants of ornaments
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