Mathematics 564

Our textbook is Algebraic Topology by Allen Hatcher. This is freely downloadable from Hatcher's web page.
Here are some suggestions for other books to look at.
- J. R. Munkres, Elements of Algebraic Topology. Covers homology and cohomology very thoroughly.
- E. H. Spanier, Algebraic Topology. One of the standard references in the field, but many people find it hard to read.
- J. P. May, A Concise Course in Algebraic Topology. The topics and presentation are interesting, but at a fairly high level.
- G. E. Bredon, Topology and Geometry. Nice book, has more on manifolds and less on homotopy theory, compared to Hatcher's book.

Due Wednesday, October 4:
1. Prove that the geometric realization of an abstract Δ-complex is the same as what Hatcher calls a Δ-complex.
2. Check that ∂_n−1 ∂_n = 0 in my definition of the chain complex for an abstract Δ-complex.
3. Section 2.1 of Hatcher (p. 131): 1, 4, 5, 8, 9, 11
Due Wednesday, October 11:
1. Section 2.1 of Hatcher (p. 131): 16, 17, 18, 19, 20
Due Wednesday, October 18:
1. Section 2.1 of Hatcher (p. 131): 19, 23, 26, 29
2. For the 5-lemma (p. 129), what are the necessary hypotheses?
Due Wednesday, October 25:
1. Read Hatcher's discussion of degree (pp. 134-137)
2. Section 2.2 of Hatcher (p. 155): 1, 2, 3, 4
Due Wednesday, November 8:
1. Section 2.2 (p. 155): choose two of 9(a), 9(b), 9(c), 9(d), 10, 12, 13
2. Section 2.2 (p. 155): choose two of 17, 20, 26, 32, 33 (note that the Mayer-Vietoris sequence works in reduced homology but only as long as the intersection is nonempty), 38 (as mentioned in class)
Due Wednesday, November 22:
1. Section 3.1 (p. 204): 2, 3, 4, 7

An equilateral triangle, barycentrically subdivided: