Errata for Algebraic and Geometric Surgery by Andrew Ranicki Oxford Mathematical Monograph (2002) This list contains corrections of misprints/errors in the book. Most of the corrections have been included in the second printing in 2003. Please let me know of any further misprints/errors by e-mail to
[email protected] A.A.R. 10.2.2007 p. 19 l. 18
ψ : Rn → V
p. 33 l. –1
i∈Z
p. 34 l. 15
dC (f ) =
p. 36 l. 17
i∈Z
p. 45 l. 13
Z[π]-module
p. 81 l. 6
arbitrary
pp. 88–89
Example 5.7. The octonion projective space O Pn is only defined for n = 1, 2, with a Hopf bundle for n = 1 only. See §3.1 of Baez (The Octonions, Bull. A.M.S. 39, 145–205 (2002)) for the construction of O P = S 8 , O P2 , and for the Hopf bundle S 7 → S 15 → S 8 .
p. 125 l. 9
I = [0, 1]
µ dD 0
(−1)i−1 f dC
¶
/0
f, M f) : · · · p. 161 l. –3 C(W
/ Z[π1 (W )]c
λ / Z[π1 (W )]c
/0
/ ··· .
p. 173 l. –1
(d + Γ)−1
p. 174 l. 6
1 Γ2 =0 .. .
0 1 Γ2 .. .
0 0 1 .. .
−1 ··· Γ ··· 0 ··· 0 .. .
d Γ 0 .. .
0 d Γ .. .
··· ··· : Ceven → Codd . ···
K1 (A)
f, M f0 )m+1−∗ ' C(W f, M f) p. 183 l. 16 C(W p. 241 l. 6
x ∈ πn+1 (f )
p. 243 l. 3
H n (C) = H n (C 0 ) = ker(d0∗ : C 0 → C 0
n
n+1
)
b −² (K) p. 248 l. 11 0 → Q p. 255
eb ² e Q² (A), e Q b ² (A) e by Q e ² (A), Q e ² (A), Q Replace Q² (A), (A) respectively. 1
¡ ¢ g ) de g : τN (x1 ) ⊕ τN (x2 ) → τM p. 259, l. 1 de g (x) = d(g(x)e g (x2 )) f(e p. 264 l. 6
embedding
p. 294 l. –4 ² = (−1)n p. 302 ll. –12,–13 Specifically, an n-connected 2n-dimensional normal map has a unique kernel form, whereas an n-connected (2n + 1)-dimensional normal map has many kernel formations. p. 311 l. –7 X 0 = X × {1} p. 326 l. –1 should read µ ¶ δ (F, G) = (F , ( , −θ)G) ∈ L2n+1 (A) . (−1)n γ ∗
p. 328 l. –7 identities p. 328 l. –4 should read µ ¶ µ ¶ γ δ ∗ (F, ( , θ)G) ⊕ (F , ( , θ)G) → ∂(G, θ) . δ (−1)n+1 γ p. 330 l. –5 replace statement of 12.36 (iii) by (iii) The effect of ` simultaneous geometric n-surgeries on (f, b) killing x1 , x2 , . . . , x` ∈ Kn (M ) is a bordant n-connected (2n + 1)-dimensional normal map (f 0 , b0 ) : M 0 → X with kernel split formation (F 0 , G0 ) obtained by algebraic surgery on (F, G) with data (H, χ, j) such that [j ∗ ] = (x1 x2 . . . x` ) : H = Z[π1 (X)]` → Kn (M ) = coker(δ : G → F ∗ ) . p. 333 l. 5
sfb r (In+1 (f ))
p. 358 l. 3
middle
p. 362 l. 4
reference [23] was published in 2002.
2
