Differential Topology

Differential Topology is the study of differentiable manifolds, spaces that locally look like an Euclidean space, but as a whole might look much different, such as for instance a sphere. Central questions we will address in this course include:

• When can a manifold be embedded into another manifold, for instance, Euclidean space?
• What can we say, globally, about the space of smooth maps from one manifold to another?
• How do submanifolds in a larger manifold intersect one another?
• How can we decompose a smooth manifold into smaller parts and obtain a more combinatorial description?

Prerequisites

No background in algebraic topology is required. Some background in point-set topology is expected. Knowledge about the basic definitions of manifolds and their tangent spaces is useful, but can be acquired during the course.

Literature

We will largely be following the following textbook:

 Morris W. Hirsch, Differential Topology, Springer GTM 33, corrected reprint, 1994.

Examination

The examination is based on weekly homework. There will be no final exam.

There will be 12 homework sets, each worth 10 points. At the end of the course, the two worst-scoring homework sets will be disregarded (this includes missed homework), for a maximum of 100 points. The grade boundaries are:

Times and dates

Tuesdays 08:15-10:00. First lecture: January 23, 2018, room D41. Last lecture: May 22, 2018.