Differential Topology

Math 7500, Winter 2017

Class:

Professor:

Resources:

Here are my notes from 1999, and here is a link to the web page for the 2012 version of the course, with detailed day by day lecture notes.

The following texts may be of interest.

Yatin has retrieved two versions of Riemann's "On the Hypotheses which Lie at the Foundations of Geometry". Spivak's translation may be easier for readers of modern English. I especially recommend section I.3, which essentially says that in an n-manifold, if we choose a coordinate function, then the subspaces along which this coordinate is constant form (n-1)-manifolds. With another coordinate function, we may then subdivide these into (n-2)-manifolds, and so on, so that with n coordinate functions, we may distinguish individual points. This indicates the generality of the local coordinates Riemann had in mind. Here are Spivak's translation and Clifford's translation.

Schedule:

You will be responsible for material covered in class, whether it is in the book or not. There will be tests.

Regular homework problems will be assigned and will be due at the start of class on the assigned due date. Their role is to strengthen your grasp on the material and fix it firmly in your memory.

Assignments:

(Text = Brocker and Janich's Introduction to Differential Topology.)