Notes from 1999 version of Math 750: Smooth Manifolds

  • Table of Contents
  • Introduction
  • Point Set Topology
  • Exercises 1
  • Reconstructing a Manifold
  • Smooth Manifolds
  • Coordinate Free Calculus
  • Exercises 2
  • Tangent Bundle
  • Exercises 3
  • Test 1
  • Vector Fields
  • Lie Groups
  • Regular Values
  • Exercises 4
  • Sards Theorem
  • Whitneys Theorem
  • Stability and Transversality
  • Smooth Approximation
  • Exercises 5
  • Riemannian Metrics
  • Manifolds with Boundary
  • Tensors
  • Differential Forms
  • Stokes Theorem