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Topological properties of manifolds with exceptional holonomy
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Topological properties of manifolds with exceptional holonomy
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Academic year 2019/2020
- Teaching staff
- Prof. Anna Maria Fino (Lecturer)
Dott. Alberto Raffero (Lecturer) - Type
- Basic
- Course disciplinary sector (SSD)
- MAT/03 - geometria
- Delivery
- Formal authority
- Language
- Italian
- Attendance
- Obligatory
- Prerequisites
- basics of Riemannian geometry, theory of principal bundles and Hodge theory
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Sommario del corso
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Course delivery
Period: January- June 2020
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Program
Program:1. Review of Riemannian G-structures and holonomy2. Clifford algebras and the group Spin(n)3. Spin structures on Riemannian manifolds, Stiefel-Whitney classes4. Chern-Weil theory, characteristic classes5. Topological properties of compact G_2-manifolds6. Topological properties of compact Spin(7)-manifoldsSuggested readings and bibliography
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- Bibliography(1) T. Friedrich. Dirac operators in Riemannian geometry. Vol. 25 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2000.(2) D. Joyce. Riemannian holonomy groups and calibrated geometry. Vol. 12 of Oxford Graduate Texts in Mathematics. Oxford University Press, Oxford, 2007.(3) S. Kobayashi, K. Nomizu. Foundations of differential geometry. Vol. II. Interscience Publishers, New York-London,1969.(4) H. B. Lawson, M.-L. Michelsohn. Spin geometry. Vol. 38 of Princeton Mathematical Series. Princeton University Press, Princeton, NJ, 1989.
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