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Complements of Discriminants of Smooth Maps: Topology and Applications: Revised Edition
 
V. A. Vassiliev Independent University of Moscow, Russia
Complements of Discriminants of Smooth Maps: Topology and Applications
Complements of Discriminants of Smooth Maps: Topology and Applications
Softcover ISBN:  978-0-8218-4618-6
Product Code:  MMONO/98
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4510-2
Product Code:  MMONO/98.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Softcover ISBN:  978-0-8218-4618-6
eBook: ISBN:  978-1-4704-4510-2
Product Code:  MMONO/98.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
Complements of Discriminants of Smooth Maps: Topology and Applications
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Complements of Discriminants of Smooth Maps: Topology and Applications
Complements of Discriminants of Smooth Maps: Topology and Applications: Revised Edition
V. A. Vassiliev Independent University of Moscow, Russia
Softcover ISBN:  978-0-8218-4618-6
Product Code:  MMONO/98
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4510-2
Product Code:  MMONO/98.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Softcover ISBN:  978-0-8218-4618-6
eBook ISBN:  978-1-4704-4510-2
Product Code:  MMONO/98.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 981992; 265 pp
    MSC: Primary 55; 57;

    This book studies a large class of topological spaces, many of which play an important role in differential and homotopy topology, algebraic geometry, and catastrophe theory. These include spaces of Morse and generalized Morse functions, iterated loop spaces of spheres, spaces of braid groups, and spaces of knots and links. Vassiliev develops a general method for the topological investigation of such spaces. One of the central results here is a system of knot invariants more powerful than all known polynomial knot invariants. In addition, a deep relation between topology and complexity theory is used to obtain the best known estimate for the numbers of branchings of algorithms for solving polynomial equations. In this revision, Vassiliev has added a section on the basics of the theory and classification of ornaments, information on applications of the topology of configuration spaces to interpolation theory, and a summary of recent results about finite-order knot invariants. Specialists in differential and homotopy topology and in complexity theory, as well as physicists who work with string theory and Feynman diagrams, will find this book an up-to-date reference on this exciting area of mathematics.

    Readership

    Physicists who work with string theory and Feynman diagrams, and specialists in differential and homotopy topology and in complexity theory.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Chapter I. Cohomology of braid groups and configuration spaces
    • Chapter II. Applications: Complexity of algorithms, superpositions of algebraic functions and interpolation theory
    • Chapter III. Topology of spaces of real functions without complicated singularities
    • Chapter IV. Stable cohomology of complements of discriminants and caustics of isolated singularities of holomorphic functions
    • Chapter V. Cohomology of the space of knots
    • Chapter VI. Invariants of ornaments
  • Additional Material
     
     
  • Reviews
     
     
    • The book is a work of stunning originality and an impressive unification of very diverse strands … [it] is carefully planned and well written.

      Zentralblatt MATH
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 981992; 265 pp
MSC: Primary 55; 57;

This book studies a large class of topological spaces, many of which play an important role in differential and homotopy topology, algebraic geometry, and catastrophe theory. These include spaces of Morse and generalized Morse functions, iterated loop spaces of spheres, spaces of braid groups, and spaces of knots and links. Vassiliev develops a general method for the topological investigation of such spaces. One of the central results here is a system of knot invariants more powerful than all known polynomial knot invariants. In addition, a deep relation between topology and complexity theory is used to obtain the best known estimate for the numbers of branchings of algorithms for solving polynomial equations. In this revision, Vassiliev has added a section on the basics of the theory and classification of ornaments, information on applications of the topology of configuration spaces to interpolation theory, and a summary of recent results about finite-order knot invariants. Specialists in differential and homotopy topology and in complexity theory, as well as physicists who work with string theory and Feynman diagrams, will find this book an up-to-date reference on this exciting area of mathematics.

Readership

Physicists who work with string theory and Feynman diagrams, and specialists in differential and homotopy topology and in complexity theory.

  • Chapters
  • Introduction
  • Chapter I. Cohomology of braid groups and configuration spaces
  • Chapter II. Applications: Complexity of algorithms, superpositions of algebraic functions and interpolation theory
  • Chapter III. Topology of spaces of real functions without complicated singularities
  • Chapter IV. Stable cohomology of complements of discriminants and caustics of isolated singularities of holomorphic functions
  • Chapter V. Cohomology of the space of knots
  • Chapter VI. Invariants of ornaments
  • The book is a work of stunning originality and an impressive unification of very diverse strands … [it] is carefully planned and well written.

    Zentralblatt MATH
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.