Differential Topology
Math 7500, Winter 2017
Class:
- Math 7500
- 218 State Hall
- MWF 9:30 - 10:20
- Text:
Brocker and Janich, Introduction to Differential Topology
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.
-
Bjorn Ian Dundas,
Differential Topology
(available online)
-
John M. Lee,
Introduction to Smooth Manifolds
(very detailed with a lot of explanation)
-
John Milnor,
Topology from the Differentiable Viewpoint
(a classic gem)
-
Guillemin and Pollack,
Differential Topology
(a standard text)
-
Abraham, Marsden and Ratiu
Manifolds, Tensor Analysis and Applications
(aimed more at applications)
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.)