Course textbooks
For Math 8301/8302, there are no assigned course textbooks. For this semester there are several reference texts which cover most of the material we will be discussing:
- Algebraic topology, by Allen Hatcher (freely available online). Hatcher's text gives an introduction to the fundamental group, homology, and cohomology.
- Algebraic topology: an introduction, by William S. Massey. This was published in 1967 and was, once, a standard textbook for an introductory course in algebraic topology. Most of our study of compact surfaces, covering spaces, and the fundamental group will be drawn from here.
- Introduction to topological manifolds, by John M. Lee. Lee's textbook gives an introduction to the theory of point-set topology and topological manifolds.
- Algebraic topology: a first course, by Greenberg and Harper. This offers an alternative perspective on the material for the first semester.
- Topology from the differentiable viewpoint, by John Milnor. This is a relatively concise (and highly influential) set of notes on differential topology.
- Lectures on algebraic topology, by Albrecht Dold. This is a slightly more difficult, but also very careful, text covering much of what is in Hatcher's textbook, but also includes some very good material on manifolds.