Applied Picard

Applied Picard

Publisher: American Mathematical Society | ISBN: 0821829483 | edition
2002 | PDF | 352 pages | 25,4 mb

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.


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