Geometry and Topology Review Questions

Fundamental Groups

Hatcher, p. 52ff, nos. 7, 8 (What is the homeomorphism type of this space?), 10, 14.

Covering Spaces

Hatcher, p. 54, no. 14 (Find all connected covering spaces), p. 79ff, nos. 4. 12. 14, 21, 27.

Basic Manifolds

Bredon, p, 76, nos. 1, 2; p. 80, nos. 1, 4; p. 82, nos. 1-3; p. 86, nos. 1-4; p. 89, nos. 1, 3.

Bundles

The text and problems of the first chapter of Alan Hatcher's text on K-theory gives a basic introduction. See

Chapters 3 and 5 of "Characteristic Classes" by Milnor & Stasheff also provide good reviews and problems.