Complements of discriminants of smooth maps : topology and applications
Author(s)
Bibliographic Information
Complements of discriminants of smooth maps : topology and applications
（Translations of mathematical monographs, v. 98）
American Mathematical Society, c1994
Rev. ed
- Other Title
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Дополнения к дискриминантам гладких отображений : топология и приложения
Dopolnenii︠a︡ k diskriminantam gladkikh otobrazheniĭ : topologii︠a︡ i prilozhenii︠a︡
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
Bibliography: p. 257-265
Description and Table of Contents
Description
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 upto-date reference on this exciting area of mathematics.
Table of Contents
Introduction Cohomology of braid groups and configuration spaces Applications: Complexity of algorithms, superpositions of algebraic functions and interpolation theory Topology of spaces of real functions without complicated singularities Stable cohomology of complements of discriminants and caustics of isolated singularities of holomorphic functions Cohomology of the space of knots Invariants of ornaments Appendix $1.$ Classifying spaces and universal bundles. Join Appendix $2.$ Hopf algebras and $H$-spaces Appendix $3.$ Loop spaces Appendix $4.$ Germs, jets, and transversality theorems Appendix $5.$ Homology of local systems Bibliography.
by "Nielsen BookData"