Buch, Englisch, Band 99, 400 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 653 g
Buch, Englisch, Band 99, 400 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 653 g
Reihe: London Mathematical Society Student Texts
ISBN: 978-1-108-72875-1
Verlag: Cambridge University Press
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.
Autoren/Hrsg.
Fachgebiete
- Naturwissenschaften Physik Quantenphysik
- Mathematik | Informatik Mathematik Topologie Algebraische Topologie
- Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Mathematik | Informatik Mathematik Algebra
Weitere Infos & Material
Part I. To A8 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.
