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Product Code:  MMONO/98 
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Softcover ISBN:  9780821846186 
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Product Code:  MMONO/98.B 
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Softcover ISBN:  9780821846186 
Product Code:  MMONO/98 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445102 
Product Code:  MMONO/98.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Softcover ISBN:  9780821846186 
eBook ISBN:  9781470445102 
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 DetailsTranslations of Mathematical MonographsVolume: 98; 1992; 265 ppMSC: 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 finiteorder 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 uptodate reference on this exciting area of mathematics.
ReadershipPhysicists 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


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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 finiteorder 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 uptodate reference on this exciting area of mathematics.
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