I'm teaching a Master's level course called "Basic Concepts in Topology and Geometry". The listed topics are:
- Topological manifolds. The fundamental group and covering spaces. Applications.
- Singular homology and applications.
- Smooth manifolds. Differential forms and Stokes’ theorem, definition of de-Rham cohomology.
Does anyone have experience teaching a course like this and have recommendations for a good textbook to use? I'd especially love a textbook that I can refer back to as the main source for our material even if I don't cover everything in class. (Or where I can make the content of the course be a certain set of chapters).
Loring Tu's book seems nice but too big for a one-semester course. Ballmann's book seems nice (though I'd need to supplement it with something about singular homology). John Lee's book seems good, but it doesn't cover differentiable manifolds.