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A Gentle Introduction to Homological Mirror Symmetry

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A Gentle Introduction to Homological Mirror Symmetry

A Gentle Introduction to Homological Mirror Symmetry

Raf Bocklandt, Universiteit van Amsterdam
August 2021
Hardback
9781108483506
    Description

    Homological 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.

    • Self-contained and accessible introduction to homological mirror symmetry, a large and complicated subject that is difficult for beginners to grasp
    • Key concepts are illustrated with simple examples to help the reader to understand the theory without being overwhelmed with technical details
    • Offers three independent perspectives on this multi-faceted subject

    Reviews & endorsements

    '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

    See more reviews

    Product details

    August 2021
    Hardback
    9781108483506
    400 pages
    235 × 158 × 29 mm
    0.764kg
    Not yet published - available from February 2025

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    Contents

    Table of Contents

    • Part 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.
      • Show more

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    About the authors
      Author
    • Raf Bocklandt , Universiteit van Amsterdam

      Raf Bocklandt is Lecturer in Mathematics at the University of Amsterdam.

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