**Prerequisites**

**Sources**

- Introduction to Smooth Manifods (Lee. GTM 218)
- Riemannian manifolds: an introduction to curvature (Lee. GTM 176). Excellent for the part of the course on connections and curvature.

- A Comprehensive Introduction to Differential Geometry (Michael Spivak). A gentle but massive five volume series, but only volume 1 is relevant.
- Calculus on Manifolds (Michael Spivak). A book for the required multivariable analysis
- Foundations of Differentiable Manifolds and Lie Groups (Warner. GTM 94)
- Will Merry wrote up some lecture notes from a previous Cambridge course which can be found on Prof. Wilson's website. The current course will be similar, but not identical.
- Lectures on Lie Groups (Adams) amazon
- Nigel Hitchin has some notes online which I highly recommend.
- A large number of detailed handouts can be found on Brian Conrad's webpage.

**Handouts**

Existence of partitions of unity (This will only be examinable under the additional assumption that the manifold is compact)

Boundary orientation
This handout fixes a silly mistake I made with regard to the definition of the orientation on the boundary

Existence of the Levi-Civita connection

**Exercise Sheets**

Exercise Sheet 1 (19 October 2011, version 2 with one added exercise)

Exercise Sheet 2 (5 December 2011, version 2 with correction to question 3 and 8)

Exercise Sheet 3 (28 November 2011)

Here is a summary of the topics that were covered in the course in 2011.