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Last updated:

November 7, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

Geometry of Manifolds analyzes topics such as the differentiable manifolds and vector fields and forms.

It also makes an introduction to Lie groups, the de Rham theorem, and Riemannian manifolds.

Course Curriculum

  • 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

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Massachusetts Institute of Technology