Frobenius manifolds and moduli spaces for singularities:
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 t...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2002
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| Schriftenreihe: | Cambridge tracts in mathematics
151 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | 1 Online-Ressource (ix, 270 Seiten) |
| ISBN: | 9780511543104 |
| DOI: | 10.1017/CBO9780511543104 |
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| 505 | 8 | 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 | ||
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Datensatz im Suchindex
| _version_ | 1804176884314931200 |
|---|---|
| any_adam_object | |
| author | Hertling, Claus |
| author_facet | Hertling, Claus |
| author_role | aut |
| author_sort | Hertling, Claus |
| author_variant | c h ch |
| building | Verbundindex |
| bvnumber | BV043941971 |
| classification_rvk | SK 370 SK 240 SK 780 |
| collection | ZDB-20-CBO |
| contents | Multiplication on the tangent bundle First examples Fast track through the results Definition and first properties of F-manifolds Finite-dimensional algebras Vector bundles with multiplication Definition of F-manifolds Decomposition of F-manifolds and examples F-manifolds and potentiality Massive F-manifolds and Lagrange maps Lagrange property of massive F-manifolds Existence of Euler fields Lyashko-Looijenga maps and graphs of Lagrange maps Miniversal Lagrange maps and F-manifolds Lyashko-Looijenga map of an F-manifold Discriminants and modality of F-manifolds Discriminant of an F-manifold 2-dimensional F-manifolds Logarithmic vector fields Isomorphisms and modality of germs of F-manifolds Analytic spectrum embedded differently Singularities and Coxeter groups Hypersurface singularities Boundary singularities Coxeter groups and F-manifolds Coxeter groups and Frobenius manifolds 3-dimensional and other F-manifolds Frobenius manifolds, Gauss-Manin connections, and moduli spaces for hypersurface singularities Construction of Frobenius manifolds for singularities Moduli spaces and other applications Connections over the punctured plane Flat vector bundles on the punctured plane Lattices Saturated lattices Riemann-Hilbert-Birkhoff problem Spectral numbers globally Meromorphic connections Logarithmic vector fields and differential forms Logarithmic pole along a smooth divisor Logarithmic pole along any divisor |
| ctrlnum | (ZDB-20-CBO)CR9780511543104 (OCoLC)849876621 (DE-599)BVBBV043941971 |
| dewey-full | 516.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/5 |
| dewey-search | 516.3/5 |
| dewey-sort | 3516.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511543104 |
| format | Electronic eBook |
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| id | DE-604.BV043941971 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511543104 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350941 |
| oclc_num | 849876621 |
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| owner | DE-12 DE-92 DE-355 DE-BY-UBR |
| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (ix, 270 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 2002 |
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| publisher | Cambridge University Press |
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| spelling | Hertling, Claus Verfasser aut Frobenius manifolds and moduli spaces for singularities Claus Hertling Frobenius Manifolds & Moduli Spaces for Singularities Cambridge Cambridge University Press 2002 1 Online-Ressource (ix, 270 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 151 Multiplication on the tangent bundle First examples Fast track through the results Definition and first properties of F-manifolds Finite-dimensional algebras Vector bundles with multiplication Definition of F-manifolds Decomposition of F-manifolds and examples F-manifolds and potentiality Massive F-manifolds and Lagrange maps Lagrange property of massive F-manifolds Existence of Euler fields Lyashko-Looijenga maps and graphs of Lagrange maps Miniversal Lagrange maps and F-manifolds Lyashko-Looijenga map of an F-manifold Discriminants and modality of F-manifolds Discriminant of an F-manifold 2-dimensional F-manifolds Logarithmic vector fields Isomorphisms and modality of germs of F-manifolds Analytic spectrum embedded differently Singularities and Coxeter groups Hypersurface singularities Boundary singularities Coxeter groups and F-manifolds Coxeter groups and Frobenius manifolds 3-dimensional and other F-manifolds Frobenius manifolds, Gauss-Manin connections, and moduli spaces for hypersurface singularities Construction of Frobenius manifolds for singularities Moduli spaces and other applications Connections over the punctured plane Flat vector bundles on the punctured plane Lattices Saturated lattices Riemann-Hilbert-Birkhoff problem Spectral numbers globally Meromorphic connections Logarithmic vector fields and differential forms Logarithmic pole along a smooth divisor Logarithmic pole along any divisor 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 Singularities (Mathematics) Frobenius algebras Moduli theory Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Tangentialbündel (DE-588)4236004-3 gnd rswk-swf Modulraum (DE-588)4183462-8 gnd rswk-swf Frobenius-Mannigfaltigkeit (DE-588)4470001-5 gnd rswk-swf Frobenius-Mannigfaltigkeit (DE-588)4470001-5 s Singularität Mathematik (DE-588)4077459-4 s Tangentialbündel (DE-588)4236004-3 s Modulraum (DE-588)4183462-8 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-81296-2 https://doi.org/10.1017/CBO9780511543104 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Hertling, Claus Frobenius manifolds and moduli spaces for singularities Multiplication on the tangent bundle First examples Fast track through the results Definition and first properties of F-manifolds Finite-dimensional algebras Vector bundles with multiplication Definition of F-manifolds Decomposition of F-manifolds and examples F-manifolds and potentiality Massive F-manifolds and Lagrange maps Lagrange property of massive F-manifolds Existence of Euler fields Lyashko-Looijenga maps and graphs of Lagrange maps Miniversal Lagrange maps and F-manifolds Lyashko-Looijenga map of an F-manifold Discriminants and modality of F-manifolds Discriminant of an F-manifold 2-dimensional F-manifolds Logarithmic vector fields Isomorphisms and modality of germs of F-manifolds Analytic spectrum embedded differently Singularities and Coxeter groups Hypersurface singularities Boundary singularities Coxeter groups and F-manifolds Coxeter groups and Frobenius manifolds 3-dimensional and other F-manifolds Frobenius manifolds, Gauss-Manin connections, and moduli spaces for hypersurface singularities Construction of Frobenius manifolds for singularities Moduli spaces and other applications Connections over the punctured plane Flat vector bundles on the punctured plane Lattices Saturated lattices Riemann-Hilbert-Birkhoff problem Spectral numbers globally Meromorphic connections Logarithmic vector fields and differential forms Logarithmic pole along a smooth divisor Logarithmic pole along any divisor Singularities (Mathematics) Frobenius algebras Moduli theory Singularität Mathematik (DE-588)4077459-4 gnd Tangentialbündel (DE-588)4236004-3 gnd Modulraum (DE-588)4183462-8 gnd Frobenius-Mannigfaltigkeit (DE-588)4470001-5 gnd |
| subject_GND | (DE-588)4077459-4 (DE-588)4236004-3 (DE-588)4183462-8 (DE-588)4470001-5 |
| title | Frobenius manifolds and moduli spaces for singularities |
| title_alt | Frobenius Manifolds & Moduli Spaces for Singularities Multiplication on the tangent bundle First examples Fast track through the results Definition and first properties of F-manifolds Finite-dimensional algebras Vector bundles with multiplication Definition of F-manifolds Decomposition of F-manifolds and examples F-manifolds and potentiality Massive F-manifolds and Lagrange maps Lagrange property of massive F-manifolds Existence of Euler fields Lyashko-Looijenga maps and graphs of Lagrange maps Miniversal Lagrange maps and F-manifolds Lyashko-Looijenga map of an F-manifold Discriminants and modality of F-manifolds Discriminant of an F-manifold 2-dimensional F-manifolds Logarithmic vector fields Isomorphisms and modality of germs of F-manifolds Analytic spectrum embedded differently Singularities and Coxeter groups Hypersurface singularities Boundary singularities Coxeter groups and F-manifolds Coxeter groups and Frobenius manifolds 3-dimensional and other F-manifolds Frobenius manifolds, Gauss-Manin connections, and moduli spaces for hypersurface singularities Construction of Frobenius manifolds for singularities Moduli spaces and other applications Connections over the punctured plane Flat vector bundles on the punctured plane Lattices Saturated lattices Riemann-Hilbert-Birkhoff problem Spectral numbers globally Meromorphic connections Logarithmic vector fields and differential forms Logarithmic pole along a smooth divisor Logarithmic pole along any divisor |
| title_auth | Frobenius manifolds and moduli spaces for singularities |
| title_exact_search | Frobenius manifolds and moduli spaces for singularities |
| title_full | Frobenius manifolds and moduli spaces for singularities Claus Hertling |
| title_fullStr | Frobenius manifolds and moduli spaces for singularities Claus Hertling |
| title_full_unstemmed | Frobenius manifolds and moduli spaces for singularities Claus Hertling |
| title_short | Frobenius manifolds and moduli spaces for singularities |
| title_sort | frobenius manifolds and moduli spaces for singularities |
| topic | Singularities (Mathematics) Frobenius algebras Moduli theory Singularität Mathematik (DE-588)4077459-4 gnd Tangentialbündel (DE-588)4236004-3 gnd Modulraum (DE-588)4183462-8 gnd Frobenius-Mannigfaltigkeit (DE-588)4470001-5 gnd |
| topic_facet | Singularities (Mathematics) Frobenius algebras Moduli theory Singularität Mathematik Tangentialbündel Modulraum Frobenius-Mannigfaltigkeit |
| url | https://doi.org/10.1017/CBO9780511543104 |
| work_keys_str_mv | AT hertlingclaus frobeniusmanifoldsandmodulispacesforsingularities AT hertlingclaus frobeniusmanifoldsmodulispacesforsingularities |