Math 545/6 Reading Guide

Here are some comments on the last two chapters of Introduction to Topological Manifolds (ITM) and suggestions for reading certain sections of Introduction to Smooth Manifolds (ISM).

In ITM Chapter 12, you should read at least to the middle of p. 318. The rest of the chapter is optional, but at least browsing it is recommended. "Proper Actions" are presented again in ISM and we will make serious study of them, so you could look at the material in ITM Chapter 12 as a preview. Example 12.28, Lens spaces, and the Universal Covering Spaces for (Compact) Surfaces are objects you should at least have a passing acquaintance with. The latter involves a bit of complex analysis.

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, of course). Glance through the chapter and read anything else that interests you.

Suggestions for reading ISM:

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Most recently updated on April 15, 2016.