Corrections to the seventh printing
of Algebraic Topology
Last updated March 12, 2008.
Below is a list of corrections, clarifications, and comments for the seventh
printing of the book (2006). Undoubtedly more errors remain to be discovered.
If you find any, please send them to me for inclusion in this list and for correcting
future printings.
- Section 1.1, page 32, third paragraph. The reference should be to Corollary
2.15 instead of 2.11. (8/21/07)
- Section 1.2, page 55, line 1. A comment: The reduced suspension depends
on the choice of basepoint, so the statement is that C is the reduced suspension
of CX with respect to a suitable choice of basepoint. (7/23/06)
- Section 1.3, page 57, third-to-last line. Change Koenig to König, to
agree with the spelling in the Bibliography and in the original source itself.
(8/21/07)
- Section 1.3, page 69, second and third lines of last paragraph. It should
say "assuming that X is path-connected, locally path-connected, and semilocally
simply-connected". (10/27/06)
- Section 2.B, page 176, Exercise 3. A better hint would be to glue two copies
of (D^n,D) to the two ends of (S^{n-1}x I,S x I) to produce a k-sphere in
S^n and then look at a Mayer-Vietoris sequence for the complement of this
k-sphere. (The hint originally given leads to problems with the point-set
topology hypotheses of the Mayer-Vietoris sequence.) (6/15/06)
- Section 3.2, page 213, third paragraph, third line. Change P^n - {0} to
P^n - {p}. (4/20/06)
- Section 3.2, page 227, first sentence. The reference to the 1980 paper of
Adams and Wilkerson is incorrect. In fact the proof of this fundamental result
has only been completed recently in work of K. Andersen and J. Grodal that
has yet to be published. (5/20/06)
- Section 3.2, page 228. The algebraic problem referred to at the end of the
first paragraph on this page has been solved. The answer is what one would
hope: The simplicial complex C_X is uniquely determined by the cohomology
ring H^*(X;Z). In fact this is true with Z_2 coefficients. A similar result
holds also in the situation mentioned in the following paragraph, so a subcomplex
of a product of n copies of CP-infinity is uniquely determined by its cohomology
ring, up to permutation of the factors (and deletion of a CP-infinity factor
if none of its positive-dimensional cells are used). The reference is Theorem
3.1 in J. Gubeladze, The isomorphism problem for commutative monoid rings,
J. Pure Appl. Alg. 129 (1998), 35-65. (12/1/07)
- Section 4.1, page 359, Exercise 22. Add the word "weakly" before
"homotopy equivalent". (3/14/07)
- Section 4.2, page 380. At the end of Example 4.50 replace K(Z,3) by K(Z,4).
(12/22/06)
- Section 4.2, page 391, line 5. H_n(X) should be H_{n+1}(X). (2/25/08)
- Section 4.3, page 400, line 6. Change h^n(point) to h_n(point). (3/3/08)
- Section 4.3, middle of page 412. In the definition of the k-invariant the
coefficient group should be pi_{n+1}(X) instead of pi_{n+1}(K). (6/15/06)
- Section 4.3, page 417, last line. The reference should be to Lemma 4.7 rather
than to an exercise in Section 4.1. (3/12/08)
- Section 4.H, page 463. Delete the extra period at the end of the first paragraph.
(5/20/06)
- Section 4.H, page 464, line 14. The superscript on D should be n rather
than m. (6/15/06)
- Section 4.I, page 468, line -19. There is a missing capital Sigma before
J_n(X). (7/7/06)