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Mathematical Surveys and Monographs
2002; 324 pp; hardcover
List Price: US$96
Member Price: US$76.80
Order Code: SURV/97
Many important functions of mathematical physics are defined as integrals depending on parameters. The Picard-Lefschetz 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 Picard-Lefschetz theory, including the classical local monodromy theory of singularities and complete intersections, Pham's generalized Picard-Lefschetz formulas, stratified Picard-Lefschetz 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 Picard-Lefschetz 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:
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.
Graduate students, research mathematicians and mathematical physicists interested in algebraic geometry, complex analysis, singularity theory, asymptotic methods, potential theory, and hyperbolic operators.
"This is a book rich in ideas ..."
-- Mathematical Reviews
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