MIT OpenCourseWare
Topics in Geometry: Dirac Geometry
Art: Johannes Kepler, Konjukce Saturnu a Jupiteru Originál, 1596 · Public domain
- Instructor
- Prof. Marco Gualtieri
- Term
- Fall 2006
- Level
- Graduate
- What's inside
- 1 lecture note · 23 other files · 2 web pages
- Materials open
- MIT OCW
About this course
Source: MIT OpenCourseWare 18.969 Topics in Geometry: Dirac Geometry, Fall 2006, Prof. Marco Gualtieri — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: none is claimed; materials are grouped by MIT's own sections. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.
Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.
Before you start
Prerequisites are not listed here. Check MIT's own syllabus for this course.
How this course was organized
What's here, and what isn't
- No lecture or session order could be confirmed for this course.
Not included here
7 items from the source could not be safely included:
- MIT's page format for this item wasn't recognized clearly enough to place it safely. (7 items)
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Lecture Notes
17 files
- The complete set of lecture notes Download
- Lecture 1: Smooth manifolds, geometry of foliations, and symplectic structure. Download
- Lecture 2: Comments on previous lecture, symplectic manifolds, and Poisson geometry. Download
- Lecture 3: Almost complex structure, Hermitian structure, integrability of J, forms on a complex manifold, and Dolbeault cohomology. Download
- Lecture 4: Geometry of V+V*, linear Dirac structures, and generalized matrices. Download
- Lecture 5: Spinors, the spin group, a bilinear pairing on spinors, and pure spinors. Download
- Lecture 6: Generalized Hodge star, and spinors for TM+T*M and the Courant algebroid. Download
- Lecture 7: Exact Courant algebroids, and Severa’s classification of exact Courant algebroids. Download
- Lecture 8: Dirac structures, and geometry of Lie groups. Download
- Lecture 9: Bilinear forms on groups. Download
- Lecture 10: Integrability, Dirac maps, and manifolds with Courant structure. Download
- Lecture 11: Integrability and spinors, and Lie bialgebroids and deformations. Download
- Lecture 12-17: Generalized complex structures and topological obstructions, intermediate cases, spinorial description, and introduction to Hermitian geometry. Download
- Lecture 18: Generalized Kahler geometry. Download
- Lecture 19: Generalized Kahler geometry, and Hodge theory on generalized Kahler manifolds. Download
- Lecture 20: Generalized complex branes of rank 1. Download
- Lecture 21-23: Linear algebra, and T-duality. Download
Assignments
MIT OpenCourseWare, Prof. Marco Gualtieri, 18.969 Topics in Geometry: Dirac Geometry, Fall 2006.
License: CC BY-NC-SA 4.0 · Edition: Fall 2006 · Open the original course on OCW ↗
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