A gentle introduction to homological mirror symmetry

    • Bocklandt, Raf

著者

    • Bocklandt, Raf

書誌事項

A gentle introduction to homological mirror symmetry

Raf Bocklandt

(London Mathematical Society student texts, 99)

Cambridge University Press, 2021

  • : hardback

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注記

Includes bibliographical references (p. 373-386) and index

内容説明・目次

内容説明

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.

目次

  • 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.

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