Applied PicardLefschetz theory
 Responsibility
 V.A. Vassiliev.
 Imprint
 Providence, RI : American Mathematical Society, c2002.
 Physical description
 xi, 324 p. : ill. ; 26 cm.
 Series
 Mathematical surveys and monographs no. 97.
Online
At the library
Science Library (Li and Ma)
Stacks
Call number  Note  Status 

QA3 .A4 NO.97  Unknown 
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Description
Creators/Contributors
 Author/Creator
 Vasilʹev, V. A., 1956
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 313320) and index.
 Contents

 Introduction Local monodromy theory of isolated singularities of functions and complete intersections Stratified PicardLefschetz theory and monodromy of hyperplane sections Newton's theorem on the nonintegrability of ovals Lacunas and local Petrovskiicondition for hyperbolic differential operators with constant coefficients Calculation of local Petrovskiicycles and enumeration of local lacunas close to real singularities Homology of local systems, twisted monodromy theory, and regularization of improper integration cycles Analytic properties of surface potentials Multidimensional hypergeometric functions, their ramification, singularities, and resonances Bibliography Index.
 (source: Nielsen Book Data)
 Publisher's summary

Many important functions of mathematical physics are defined as integrals depending on parameters. The PicardLefschetz theory studies how analytic and qualitative properties of such integrals (regularity, algebraicity, ramification, singular points, etc.) depend on the monodromy of corresponding integration cycles. In this book, V. A. Vassiliev presents several versions of the PicardLefschetz theory, including the classical local monodromy theory of singularities and complete intersections, Pham's generalized PicardLefschetz formulas, stratified PicardLefschetz theory, and also twisted versions of all these theories with applications to integrals of multivalued forms. The author also shows how these versions of the PicardLefschetz theory are used in studying a variety of problems arising in many areas of mathematics and mathematical physics.In particular, he discusses the following classes of functions: volume functions arising in the ArchimedesNewton problem of integrable bodies; NewtonCoulomb potentials; fundamental solutions of hyperbolic partial differential equations; and, multidimensional hypergeometric functions generalizing the classical Gauss hypergeometric integral. The book is geared toward a broad audience of graduate students, research mathematicians and mathematical physicists interested in algebraic geometry, complex analysis, singularity theory, asymptotic methods, potential theory, and hyperbolic operators.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2002
 Series
 Mathematical surveys and monographs, 00765376 ; v. 97
 ISBN
 0821829483 (alk. paper)
 9780821829486 (acidfree paper)