# LECTURE NOTES

## Geometry and Topology I (Math 208)
Fall 2005, UCSCU

- Lecture Notes
  Definition of manifolds. Examples. History.

- Lecture Notes 2 A
  IFTs as giving coordinates.

- Lecture Notes 3
  The tangent space at a point.

- Lecture Notes 4
  Covectors. Cotangent Space. Vector Fields

- Lecture Notes 5
  Immersions, submersions, embeddings.

- Lecture Notes of McCain
  Sard's theorem. Whitney embeddings. Nice excursions into space-filling curves.

- Lecture Notes 6
  Flows. Lie bracket via flows.

- Lecture Notes 7
  Smooth group actions. Homogeneous spaces. !UPDATED. Nov 14.

- Lecture Notes 7
  *** gotta enter this one still** `fun': pf of Fund Thm Alg; and of Brouwer fixed pt, from Milnor

- Lecture Notes 8
  last lecture notes Frobenius thm. distributions. subbundles. straightening lemma