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Geometry of Manifolds analyzes topics such as the differentiable manifolds and vector fields and forms.
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English
English [CC]
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Description
It also makes an introduction to Lie groups, the de Rham theorem, and Riemannian manifolds.
Course content
- Manifolds: Definitions and Examples Unlimited
- Smooth Maps and the Notion of Equivalence Standard Pathologies Unlimited
- The Derivative of a Map between Vector Spaces Unlimited
- Inverse and Implicit Function Theorems Unlimited
- More Examples Unlimited
- Vector Bundles and the Differential: New Vector Bundles from Old Unlimited
- Vector Bundles and the Differential: The Tangent Bundle Unlimited
- Connections Unlimited
- The Embedding Manifolds in RN Unlimited
- Sard’s Theorem Unlimited
- Stratified Spaces Unlimited
- Fiber Bundles Unlimited
- Whitney’s Embedding Theorem, Medium Version Unlimited
- A Brief Introduction to Linear Analysis: Basic Definitions Unlimited
- A Brief Introduction to Linear Analysis: Fredholm Operators Unlimited
- Smale’s Sard Theorem Unlimited
- Parametric Transversality Unlimited
- The Strong Whitney Embedding Theorem Unlimited
- Morse Theory Unlimited
- Canonical Forms: The Lie Derivative Unlimited
- Canonical Forms: The Frobenious Integrability Theorem Unlimited
- Differential Forms and de Rham’s Theorem: The Exterior Algebra Unlimited
- Differential Forms and de Rham’s Theorem Unlimited
- Refinement The Acyclicity of the Sheaf of p-forms Unlimited
- The Poincaré Lemma Implies the Equality of Cech Cohomology and de Rham Cohomology Unlimited
- The Immersion Theorem of Smale Unlimited
Instructor
Massachusetts Institute of Technology
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