Effective Constructive Algebraic Topology - Institut Fourier

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The same for P ∞ C ? Topological version ? Easy. P ∞ C = X = lim→ X2n where: X2n = X2n−2 ∪ f 2n D 2n with: D 2n ⊃ S 2n−1 → P n−1 C the canonical projection. Simplicial version? Much harder! 8
Easy up to homotopy. Easiest solution = K(Z, 2). Justification = two principal fibrations: S 1 ↩→ S ∞ −→ P ∞ C K(Z, 1) ↩→ E(Z, 1) −→ K(Z, 2) + (K(Z, 1) ∼ S 1 )+(S ∞ contractible) +(E(Z, 1) contractible) ⇒ P ∞ C ∼ K(Z, 2) Remark: K(Z, 2) not of finite type! Simplicial model of finite type for P 2 C?? 9
Page 1 and 2: Effective Constructive Algebraic To
Page 3 and 4: Three solutions for Constructive Al
Page 5 and 6: Notion of CW-Complex X: X = lim −
Page 7 and 8: Example 2. More generally: 1. X0 =
Page 9: Simplicial version of P ∞ R: P
Page 13 and 14: CW-complex: X = lim Xn = {(D → n
Page 15 and 16: Theorem (Adams, 1956): Let X be a 1
Page 17: Chapter 13 Stable Homotopy and Iter
Page 20 and 21: Kenzo computing d5 : [C5(Ω 3 ) =
Page 22 and 23: Analysis of the problem: “Standar
Page 24 and 25: Definition: A (homological) reducti
Page 26 and 27: ρ: h C∗ C∗ g f 1. What is Hn(

Effective Constructive Algebraic Topology - Institut Fourier

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