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Catalogue Information
Field name	Details
Dewey Class	516.35
Title	Isomonodromic Deformations and Frobenius Manifolds ([Ebook]) : An Introduction / by Claude Sabbah.
Author	Sabbah, Claude
Other name(s)	SpringerLink (Online service)
Publication	London : Springer , 2008.
Physical Details	: online resource.
Series	Universitext
ISBN	9781848000544
Summary Note	The notion of a Frobenius structure on a complex analytic manifold appeared at the end of the seventies in the theory of singularities of holomorphic functions. Motivated by physical considerations, further development of the theory has opened new perspectives on, and revealed new links between, many apparently unrelated areas of mathematics and physics. Based on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations and ends with applications to recent research questions related to mirror symmetry. The fundamental tool used within the book is that of a vector bundle with connection. There is a detailed analysis of the singularities of such objects and of their deformations, and coverage of the techniques used in the resolution of the Riemann-Hilbert problem and Birkhoffâs problem. An approach to Frobenius manifolds using isomonodromic deformations of linear differential equations is also developed. Aimed at graduate students and researchers, the book assumes some familiarity with basic complex algebraic geometry.:
Contents note	The language of fibre bundles -- Holomorphic vector bundles on the Riemann sphere -- The Riemann-Hilbert correspondence -- Lattices -- The Riemann-Hilbert problem and Birkhoff's problem -- Fourier-Laplace duality -- Integrable deformations -- Saito structures and Frobenius structures -- References -- Index of notation -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-1-84800-054-4
Links to Related Works	Subject References: Algebraic Geometry . Geometry, Algebraic . Mathematics . Mathematics, general . Authors: Sabbah, Claude . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 516.35 . 516.35 (DDC 22) .

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Isomonodromic Deformations and Frobenius Manifolds: An Introduction

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