What are the prerequisites for Differential Topology?

Question

I'm looking to do some independent reading and I haven't been able to find rough prerequisites for Differential Topology at the level of Milnor or Guillemin and Pollack.

Is a semester of analysis (Pugh) and a semester of topology (Munkres) enough to make sense of most of it or should I take a second semester of analysis first?

Answer 1

If you understand some set theory, you might like to use Kinsey's "Topology of Surfaces", which is what my class used as a pre/corequisite when we were studying Milnor's "Topology from the Differentiable Viewpoint".

They complement each-other nicely; Kinsey is tutorial-like and you could probably get through five pages in a day, whereas Milnor is terse and one page a day (depending on the page!) is a fast self-study pace.

Answer 2

GP itself says a year of analysis and a semester of linear algebra, but based on speeds and all. I'm taking a class based on those books, and what matters most is that you know rigorous multivariable calculus well (Chapter 5 in your Pugh).