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Handbook of Geometry and Topology of Singularities I
Taschenbuch von José Luis Cisneros Molina (u. a.)
Sprache: Englisch

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Beschreibung
This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways.

Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject.

This is the first volume in a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research.

The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways.

Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject.

This is the first volume in a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research.

The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
Über den Autor

José Luis Cisneros-Molina (PhD, University of Warwick 1999) is a full-time researcher at the Mathematics Institute of the National Autonomous University of Mexico. His research interests are in Algebraic and Differential Topology, Differential Geometry and Singularity Theory, with a particular focus on generalizations of Milnor Fibrations for complex and real analytic maps.

D¿ng Tráng Lê (PhD, University of Paris 1969) is an Emeritus Professor at Aix-Marseille University. Previously he was Professor at the Universities of Paris VII (1975-1999) and Marseille, and was head of Mathematics at the ICTP at Trieste. One of the founders of modern Singularity Theory, he has made numerous contributions to morsification, the topology of complex singularities, polar varieties, carousels, among other topics.

José Seade (DPhil, University of Oxford 1980) is a full-time researcher at the Mathematics Institute of the National Autonomous University of Mexico. His researchis in the theory of indices of vector fields and Chern classes for singular varieties, with applications to foliations, and Milnor's fibration theorem for analytic maps. In 2007 he was awarded the Ferran Sunyer i Ballaguer prize.

Zusammenfassung

Presents in-depth and accessible surveys of topics in singularity theory, including their interrelationships and connections with other subjects

Ideal for graduate students and researchers in general who want to learn about this active field, and as a reference for specialists

Emphasizes clarity and quality of exposition rather than technical details

Encourages readers to go deeper into the subject by offering illuminating insights and useful bibliographies

Inhaltsverzeichnis
Foreword.- Preface.- 1 The Combinatorics of Plane Curve Singularities.- 2 The Topology of Surface Singularities.- 3 Resolution of Singularities: an Introduction.- 4 Stratification Theory.- 5 Morse Theory, Stratification and Sheaves.- 6 The Topology of the Milnor Fibration.- 7 Deformation and Smoothing of Singularities.- 8 Distinguished Bases and Monodromy of Complex Hypersurface Singularities.- 9 The Lefschetz Theorem for Hyperplane Sections.- 10 Finite Dimensional Lie Algebras in Singularities. -Index.
Details
Erscheinungsjahr: 2021
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xviii
601 S.
74 s/w Illustr.
54 farbige Illustr.
601 p. 128 illus.
54 illus. in color.
ISBN-13: 9783030530631
ISBN-10: 3030530639
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Redaktion: Cisneros Molina, José Luis
Lê, D¿ng Tráng
Seade, José
Herausgeber: José Luis Cisneros Molina/Dung Tráng Lê/José Seade
Auflage: 1st ed. 2020
Hersteller: Springer International Publishing
Springer International Publishing AG
Maße: 235 x 155 x 34 mm
Von/Mit: José Luis Cisneros Molina (u. a.)
Erscheinungsdatum: 26.10.2021
Gewicht: 0,925 kg
Artikel-ID: 120648524
Über den Autor

José Luis Cisneros-Molina (PhD, University of Warwick 1999) is a full-time researcher at the Mathematics Institute of the National Autonomous University of Mexico. His research interests are in Algebraic and Differential Topology, Differential Geometry and Singularity Theory, with a particular focus on generalizations of Milnor Fibrations for complex and real analytic maps.

D¿ng Tráng Lê (PhD, University of Paris 1969) is an Emeritus Professor at Aix-Marseille University. Previously he was Professor at the Universities of Paris VII (1975-1999) and Marseille, and was head of Mathematics at the ICTP at Trieste. One of the founders of modern Singularity Theory, he has made numerous contributions to morsification, the topology of complex singularities, polar varieties, carousels, among other topics.

José Seade (DPhil, University of Oxford 1980) is a full-time researcher at the Mathematics Institute of the National Autonomous University of Mexico. His researchis in the theory of indices of vector fields and Chern classes for singular varieties, with applications to foliations, and Milnor's fibration theorem for analytic maps. In 2007 he was awarded the Ferran Sunyer i Ballaguer prize.

Zusammenfassung

Presents in-depth and accessible surveys of topics in singularity theory, including their interrelationships and connections with other subjects

Ideal for graduate students and researchers in general who want to learn about this active field, and as a reference for specialists

Emphasizes clarity and quality of exposition rather than technical details

Encourages readers to go deeper into the subject by offering illuminating insights and useful bibliographies

Inhaltsverzeichnis
Foreword.- Preface.- 1 The Combinatorics of Plane Curve Singularities.- 2 The Topology of Surface Singularities.- 3 Resolution of Singularities: an Introduction.- 4 Stratification Theory.- 5 Morse Theory, Stratification and Sheaves.- 6 The Topology of the Milnor Fibration.- 7 Deformation and Smoothing of Singularities.- 8 Distinguished Bases and Monodromy of Complex Hypersurface Singularities.- 9 The Lefschetz Theorem for Hyperplane Sections.- 10 Finite Dimensional Lie Algebras in Singularities. -Index.
Details
Erscheinungsjahr: 2021
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xviii
601 S.
74 s/w Illustr.
54 farbige Illustr.
601 p. 128 illus.
54 illus. in color.
ISBN-13: 9783030530631
ISBN-10: 3030530639
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Redaktion: Cisneros Molina, José Luis
Lê, D¿ng Tráng
Seade, José
Herausgeber: José Luis Cisneros Molina/Dung Tráng Lê/José Seade
Auflage: 1st ed. 2020
Hersteller: Springer International Publishing
Springer International Publishing AG
Maße: 235 x 155 x 34 mm
Von/Mit: José Luis Cisneros Molina (u. a.)
Erscheinungsdatum: 26.10.2021
Gewicht: 0,925 kg
Artikel-ID: 120648524
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