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OverviewHomological mirror symmetry has its origins in theoretical physics but is now of great interest in mathematics due to the deep connections it reveals between different areas of geometry and algebra. This book offers a self-contained and accessible introduction to the subject via the representation theory of algebras and quivers. It is suitable for graduate students and others without a great deal of background in homological algebra and modern geometry. Each part offers a different perspective on homological mirror symmetry. Part I introduces the A-infinity formalism and offers a glimpse of mirror symmetry using representations of quivers. Part II discusses various A- and B-models in mirror symmetry and their connections through toric and tropical geometry. Part III deals with mirror symmetry for Riemann surfaces. The main mathematical ideas are illustrated by means of simple examples coming mainly from the theory of surfaces, helping the reader connect theory with intuition. Full Product DetailsAuthor: Raf Bocklandt (Universiteit van Amsterdam)Publisher: Cambridge University Press Imprint: Cambridge University Press Dimensions: Width: 15.80cm , Height: 2.90cm , Length: 23.50cm Weight: 0.764kg ISBN: 9781108483506ISBN 10: 110848350 Pages: 400 Publication Date: 19 August 2021 Audience: Professional and scholarly , College/higher education , Professional & Vocational , Tertiary & Higher Education Format: Hardback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsPart I. To A∞ and Beyond: 1. Categories; 2. Cohomology; 3. Higher products; 4. Quivers; Part II. A Glance through the Mirror: 5. Motivation from physics; 6. The A-side; 7. The B-side; 8. Mirror symmetry; Part III. Reflections on Surfaces: 9. Gluing; 10. Grading; 11. Stabilizing; 12. Deforming; References; Index.Reviews'Each chapter concludes with a few exercises, and great care has been taken to use notation and terminology in a consistent way. That must have taken considerable effort and it greatly increases the value of the book because there are many examples in mirror symmetry of different writers using the same words to mean different, often subtly different, things.' G. K. Sankaran, MathSciNet 'The book under review provides an introduction to homological mirror symmetry which is accessible to graduate students in mathematics. In particular, it includes a great amount of background material, and motivational sections. Among the reason it is so approachable is the style ...' Hulya Arguz, zbMATH Author InformationRaf Bocklandt is Lecturer in Mathematics at the University of Amsterdam. Tab Content 6Author Website:Countries AvailableAll regions |
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