ERRATA: A CONCISE COURSE IN ALGEBRAIC TOPOLOGY

J.P. MAY

I thank Gaunce Lewis, Michael Spertus, and Anna Marie Bohmann for catching some of the following mistakes and misprints. I welcome further corrections and comments.

Page 6, line 13: to be the constant loop ... [add “be”] Page 30, line 23: and, if we choose a basepoint u in U ... [delete “each”] Page 49: locally finite is incorrectly defined: each b ∈ B should have a neighbor-

hood that intersects only finitely many U ∈ 𝒪. This is needed for the continuity argument at the end of the proof of the Theorem stated on this page.

Page 76: The proof of the Theorem stated on this page is not correct unless A is path connected, and there is a misprint in the display four lines from the bottom. To fix both things, replace the cited display and the rest of the sentence in which it occurs with the following material:

X_{0} = ΓA ∨ ( ⋁_{(q,j)} S^{q}),

where {(q, j)} runs over q ≥ 1 and based maps j : S^{q} ⟶ X that represent generators of π_{q}(X). Here the chosen basepoint is in ΓA. Construct γ_{0} : X_{0} ⟶ X using the maps j and the given map γ : ΓA ⟶ A. Construct X_{1} from X_{0} by choosing a point in each non-basepoint component of ΓA and attaching intervals to connect the chosen points to the basepoint. Paths in X that connect the images of the chosen points under γ to the basepoint of X give γ_{1} : X_{1} ⟶ X extending γ_{0}. From here, the construction continues exactly as in §5.

Page 77, line 1: Replace A and X by ΓA and ΓX. Page 80, diagram: Replace the source and target of e by A and A′, respectively. Page 86, line 15: Replace I_{q} by I^{q}. Page 139, line -14: Replace g : ℝ^{m} ⟶ ℝ^{n} by g : S^{m} ⟶ S^{n} Page 154, line 7: u_{i} and u_{j} should be z_{i} and z_{j} Page 157, line 8: H_{i}(U_{1} ∪ ⋯ ∪ U_{q}) = 0 Page 159, line -9: Replace H_{0}(ℝ_{n}) by H_{0}(ℝ^{n}) Page 177: in the first diagram, the last map should be (id ∧ ϕ_{p,q})_{∗}(t ∧ id)_{∗} rather

than (id ∧ ϕ_{p,q})_{∗}(id ∧ t)_{∗} Page 179, bottom right of diagram: Change K(π_{1}, 3) to K(π_{2}, 3) Page 188, bottom line: z ∈ H_{n}(M; ℤ_{2}) Page 194, line 21 2n-plane in ℝ^{∞} Page 207, line -4: [X_{+}, BU(1)] ≅ H^{2}(X; ℤ). Page 210, line 3: Change (1 + ξ_{1}) ⋯ (1 + ξ_{n}) to (1 + ξ_{1}t) ⋯ (1 + ξ_{n}t) Page 217, line -11: Replace g^{−1}(E(ν)) with g^{−1}(E(γ_{q}^{r})) Page 223, line 9: sq^{I} should be Sq^{I} Page 228, fourth line of Definition: change σ′_{n} ∘ ΣT_{n} to σ′_{n} ∘ Σf_{n} Page 238, line -4: change §16 to §17