Singularities of Differentiable Maps, Volume 2 Monodromy and Asymptotics of Integrals /

Originally published in the 1980s, Singularities of Differentiable Maps: Monodromy and Asymptotics of Integrals was the second of two volumes that together formed a translation of the authors' influential Russian monograph on singularity theory. This uncorrected softcover reprint of the work br...

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Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Arnold, Elionora (Author), Gusein-Zade, S.M (Author), Varchenko, Alexander N. (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:Inglés
Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2012.
Edition:1st ed. 2012.
Series:Modern Birkhäuser Classics,
Subjects:
Mathematical analysis.
Algebraic geometry.
Geometry, Differential.
Topological groups.
Lie groups.
Manifolds (Mathematics).
Mathematics.
Analysis.
Algebraic Geometry.
Differential Geometry.
Topological Groups and Lie Groups.
Manifolds and Cell Complexes.
Applications of Mathematics.
Online Access:Texto Completo
Table of Contents:
  • Part I. The topological structure of isolated critical points of functions
  • Introduction
  • Elements of the theory of Picard-Lefschetz
  • The topology of the non-singular level set and the variation operator of a singularity
  • The bifurcation sets and the monodromy group of a singularity
  • The intersection matrices of singularities of functions of two variables
  • The intersection forms of boundary singularities and the topology of complete intersections
  • Part II. Oscillatory integrals
  • Discussion of results
  • Elementary integrals and the resolution of singularities of the phase
  • Asymptotics and Newton polyhedra
  • The singular index, examples
  • Part III. Integrals of holomorphic forms over vanishing cycles
  • The simplest properties of the integrals
  • Complex oscillatory integrals
  • Integrals and differential equations
  • The coefficients of series expansions of integrals, the weighted and Hodge filtrations and the spectrum of a critical point
  • The mixed Hodge structure of an isolated critical point of a holomorphic function
  • The period map and the intersection form
  • References
  • Subject Index.

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