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5 produkter
5 produkter
Inbunden, Engelska, 2023
814 kr
Skickas inom 10-15 vardagar
This textbook, based on a one-semester course taught several times by the authors, provides a self-contained, comprehensive yet concise introduction to the theory of pseudoholomorphic curves. Gromov’s nonsqueezing theorem in symplectic topology is taken as a motivating example, and a complete proof using pseudoholomorphic discs is presented. A sketch of the proof is discussed in the first chapter, with succeeding chapters guiding the reader through the details of the mathematical methods required to establish compactness, regularity, and transversality results. Concrete examples illustrate many of the more complicated concepts, and well over 100 exercises are distributed throughout the text. This approach helps the reader to gain a thorough understanding of the powerful analytical tools needed for the study of more advanced topics in symplectic topology.This text can be used as the basis for a graduate course, and it is also immensely suitable for independentstudy. Prerequisites include complex analysis, differential topology, and basic linear functional analysis; no prior knowledge of symplectic geometry is assumed.This book is also part of the Virtual Series on Symplectic Geometry.
Engelska, 2023
648 kr
Skickas inom 5-8 vardagar
Häftad, Engelska, 2024
599 kr
Skickas inom 10-15 vardagar
This textbook, based on a one-semester course taught several times by the authors, provides a self-contained, comprehensive yet concise introduction to the theory of pseudoholomorphic curves. Gromov’s nonsqueezing theorem in symplectic topology is taken as a motivating example, and a complete proof using pseudoholomorphic discs is presented. A sketch of the proof is discussed in the first chapter, with succeeding chapters guiding the reader through the details of the mathematical methods required to establish compactness, regularity, and transversality results. Concrete examples illustrate many of the more complicated concepts, and well over 100 exercises are distributed throughout the text. This approach helps the reader to gain a thorough understanding of the powerful analytical tools needed for the study of more advanced topics in symplectic topology.This text can be used as the basis for a graduate course, and it is also immensely suitable for independentstudy. Prerequisites include complex analysis, differential topology, and basic linear functional analysis; no prior knowledge of symplectic geometry is assumed.This book is also part of the Virtual Series on Symplectic Geometry.
Häftad, Tyska, 2026
350 kr
Kommande
Das vorliegende, auf zwei Bände angelegte Lehrbuch folgt einer zweisemestrigen Vorlesung über Lineare Algebra. Dabei wird ein geometrischer Zugang zu vielen der algebraischen Themen gewählt. So werden zum Beispiel lineare Abbildungen ausführlich anhand der Geometrie der Ebene und des dreidimensionalen Raumes motiviert, und Determinanten werden als Volumina interpretiert.Ein Einführungskapitel behandelt einige schulgeometrische Aspekte vom höheren Standpunkt aus und gibt einen ersten Einblick in die Wirkmacht linear algebraischer Methoden, insbesondere im Hinblick auf elementargeometrische Überlegungen. Die weiteren Kapitel decken die Grundlagen und Theorie bis zur Hauptachsentransformation ab. Ein besonderer Fokus liegt auf der Theorie der euklidischen Vektorräume, einschließlich vielfältiger Anwendungen auf die klassische Dreiecksgeometrie. Zahlreiche in den Text eingefügte Übungsaufgaben laden zum aktiven Lesen ein, und Verweise auf Originalquellen liefern historischen Kontext.Ob zum Selbststudium oder als Begleitung für die Vorlesung, ob zum direkten Einsatz in der Lehre oder als Inspirationsquelle, dieses reich bebilderte Lehrbuch überzeugt durch seine präzise, aber nie überformalisierte Sprache und eine moderne und ansprechende Darstellung.
Häftad, Engelska, 2026
670 kr
Kommande
This first course on differential geometry includes not only Riemannian manifolds, but also symplectic and contact geometry. Rather than treating these three fields of geometry as separate subjects, this text emphasises common features by organising the material according to ideas and methods shared by the three fields.Specifically, this text highlights how certain concepts, such as structure-preserving vector fields or variational characterisations of curves adapted to a given geometric structure, find their analogous expressions in the respective field of geometry. For example, Frobenius integrability, which is primarily relevant for contact geometry, is discussed together with the classification of flat Riemannian manifolds, which requires very similar arguments.Another case in point is the discussion of transformation groups (isometries, symplectomorphisms, contactomorphisms) and the corresponding Lie algebras. Two equivalent ways to construct this Lie algebra structure are described: from the usual Lie bracket of vector fields on the manifold, restricted to the subalgebra of structure-preserving ones, or from the right-invariant vector fields on the transformation group.This book also provides a concise introduction to manifolds, vector bundles, differential forms and tensors. As a result, it contains more material than can be covered in a single semester, and it is possible to teach various courses from it, depending on the background knowledge one may want to assume. Many examples and exercises are integrated into the richly illustrated text, making the book suitable for self-study.