Math 545/6 Reading Guide

Here are some comments on last two chapters of Introduction to Topological Manifolds (ITM) that I made in class.

In ITM Chapter 12, you should read at least to the middle of p. 316. The rest of the chapter is optional. If you would like to see some more examples of covering spaces, I recommend Classification of Torus Coverings (Prop. 12.20), Lens spaces (Ex. 12.28), and the Universal Covering Spaces for (Compact) Surfaces (Thm. 12.29 & 12.30). The latter involves some complex analysis and hyperbolic geometry.

"Proper Actions" are presented again in ISM and we will make serious study of them there.

ITM Chapter 13 is completely optional. For a very brief view of some aspects of homology, now or later, read the introduction, pp. 339-340, and the section on homology of spheres, pp. 364-369 (skipping the proofs). Glance through the chapter and read anything else that interests you.

Some comments on reading ISM

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Most recently updated on April 8, 2018.