Complements of Discriminants of Smooth Maps: Topology and Applications 论文

摘要

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.