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 |
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 |
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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 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.
ReadershipPhysicists who work with string theory and Feynman diagrams, and specialists in differential and homotopy topology and in complexity theory.
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Table of Contents
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Chapters
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Introduction
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Chapter I. Cohomology of braid groups and configuration spaces
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Chapter II. Applications: Complexity of algorithms, superpositions of algebraic functions and interpolation theory
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Chapter III. Topology of spaces of real functions without complicated singularities
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Chapter IV. Stable cohomology of complements of discriminants and caustics of isolated singularities of holomorphic functions
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Chapter V. Cohomology of the space of knots
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Chapter VI. Invariants of ornaments
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Additional Material
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Reviews
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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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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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.
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