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Frobenius manifolds and moduli spaces for singularities /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Frobenius manifolds and moduli spaces for singularities // Claus Hertling.
其他題名:	Frobenius Manifolds & Moduli Spaces for Singularities
作者:	Hertling, Claus,
面頁冊數:	1 online resource (ix, 270 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Moduli theory. -
電子資源:	https://doi.org/10.1017/CBO9780511543104
ISBN:	9780511543104 (ebook)

Frobenius manifolds and moduli spaces for singularities /
Hertling, Claus,

Frobenius manifolds and moduli spaces for singularities /Frobenius Manifolds & Moduli Spaces for SingularitiesClaus Hertling. - 1 online resource (ix, 270 pages) :digital, PDF file(s). - Cambridge tracts in mathematics ;151. - Cambridge tracts in mathematics ;203..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Multiplication on the tangent bundle --

The relations between Frobenius manifolds and singularity theory are treated here in a rigorous yet accessible manner. For those working in singularity theory or other areas of complex geometry, this book will open the door to the study of Frobenius manifolds. This class of manifolds are now known to be relevant for the study of singularity theory, quantum cohomology, mirror symmetry, symplectic geometry and integrable systems. The first part of the book explains the theory of manifolds with a multiplication on the tangent bundle. The second presents a simplified explanation of the role of Frobenius manifolds in singularity theory along with all the necessary tools and several applications. Readers will find here a careful and sound study of the fundamental structures and results in this exciting branch of maths. This book will serve as an excellent resource for researchers and graduate students who wish to work in this area.

ISBN: 9780511543104 (ebook)Subjects--Topical Terms:

681816
Moduli theory.

LC Class. No.: QA614.58 / .H47 2002

Dewey Class. No.: 516.3/5

Frobenius manifolds and moduli spaces for singularities /
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 0 $t Multiplication on the tangent bundle -- $t First examples -- $t Fast track through the results -- $t Definition and first properties of F-manifolds -- $t Finite-dimensional algebras -- $t Vector bundles with multiplication -- $t Definition of F-manifolds -- $t Decomposition of F-manifolds and examples -- $t F-manifolds and potentiality -- $t Massive F-manifolds and Lagrange maps -- $t Lagrange property of massive F-manifolds -- $t Existence of Euler fields -- $t Lyashko-Looijenga maps and graphs of Lagrange maps -- $t Miniversal Lagrange maps and F-manifolds -- $t Lyashko-Looijenga map of an F-manifold -- $t Discriminants and modality of F-manifolds -- $t Discriminant of an F-manifold -- $t 2-dimensional F-manifolds -- $t Logarithmic vector fields -- $t Isomorphisms and modality of germs of F-manifolds -- $t Analytic spectrum embedded differently -- $t Singularities and Coxeter groups -- $t Hypersurface singularities -- $t Boundary singularities -- $t Coxeter groups and F-manifolds -- $t Coxeter groups and Frobenius manifolds -- $t 3-dimensional and other F-manifolds -- $t Frobenius manifolds, Gauss-Manin connections, and moduli spaces for hypersurface singularities -- $t Construction of Frobenius manifolds for singularities -- $t Moduli spaces and other applications -- $t Connections over the punctured plane -- $t Flat vector bundles on the punctured plane -- $t Lattices -- $t Saturated lattices -- $t Riemann-Hilbert-Birkhoff problem -- $t Spectral numbers globally -- $t Meromorphic connections -- $t Logarithmic vector fields and differential forms -- $t Logarithmic pole along a smooth divisor -- $t Logarithmic pole along any divisor.
520 $a The relations between Frobenius manifolds and singularity theory are treated here in a rigorous yet accessible manner. For those working in singularity theory or other areas of complex geometry, this book will open the door to the study of Frobenius manifolds. This class of manifolds are now known to be relevant for the study of singularity theory, quantum cohomology, mirror symmetry, symplectic geometry and integrable systems. The first part of the book explains the theory of manifolds with a multiplication on the tangent bundle. The second presents a simplified explanation of the role of Frobenius manifolds in singularity theory along with all the necessary tools and several applications. Readers will find here a careful and sound study of the fundamental structures and results in this exciting branch of maths. This book will serve as an excellent resource for researchers and graduate students who wish to work in this area.
650 0 $a Moduli theory. $3 681816
650 0 $a Frobenius algebras. $3 579819
650 0 $a Singularities (Mathematics) $3 527840
776 0 8 $i Print version: $z 9780521812962
830 0 $a Cambridge tracts in mathematics ; $v 203. $3 1238301
856 4 0 $u https://doi.org/10.1017/CBO9780511543104