Coming soon
This note is part of the planned structure of the general relativity sequence and has not been written yet.
This section page is a stable landing point; the sub-topics below will be filled in over time.
Sequence
- 01. Orientation, Volume Form, the Hodge Star
- 02. The Codifferential and the Laplace-de Rham Operator
- 03. Hodge Decomposition; de Rham Cohomology
- 04. Conformal Transformations and Weyl Rescaling
- 05. Almost-Complex and Complex Manifolds
- 06. Hermitian and Kahler Manifolds
- 07. Where This Surfaces in GR (self-duality, Euclidean methods, twistors)
- 08. Characteristic Classes and Chern-Weil Theory
- 09. Self-Dual and Anti-Self-Dual Two-Forms in Four Dimensions
- 10. The Atiyah-Singer Index Theorem and the Dirac Operator
- 11. Bochner-Weitzenbock Identities and Vanishing Theorems
- 12. Hodge Theory in Lorentzian Signature
- 13. Calabi-Yau and Special Holonomy
- 14. Homotopy and the Fundamental Group
- 15. Covering Spaces and Higher Homotopy Groups
- 16. Singular Homology and Poincare Duality
- 17. Differential Topology (Morse Theory, Degree, Poincare-Hopf)