Complements of discriminants of smooth maps: topology and applications / V. A. Vassiliev

Auteur: Vassiliev, Victor Anatolievich (1956-) - AuteurAuteur secondaire : Godfard, B. - Traducteur ; Gelfand, Sergei Izrailevich (1944-) - TraducteurType de document: MonographieCollection: Translations of mathematical monographs ; 98Langue: anglaisPays: Etats UnisÉditeur: Providence : American Mathematical Society, 1994Edition: revised editionDescription: 1 vol. (IX-265 p.) : appendix ; 27 cm ISBN: 9780821846186 ; br. Résumé: 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. (source : AMS).Bibliographie: Bibliogr. p. 257-265. Sujets MSC: 55S40 Algebraic topology -- Operations and obstructions -- Sectioning fiber spaces and bundles
55Txx Algebraic topology -- Spectral sequences
57R45 Manifolds and cell complexes -- Differential topology -- Singularities of differentiable mappings
57M25 Manifolds and cell complexes -- Low-dimensional topology -- Knots and links in S3
68Q25 Computer science -- Theory of computing -- Analysis of algorithms and problem complexity
En-ligne: Zentralblatt | MathSciNet | AMS
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Bibliogr. p. 257-265

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. (source : AMS)

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