Effective Constructive Algebraic Topology - Institut Fourier

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Semantics of colours: Blue = “Standard” Mathematics Red = Constructive, effective, algorithm, machine object, . . . Violet = Problem, difficulty, obstacle, disadvantage, . . . Green = Solution, essential point, mathematicians, . . . 0
Three solutions for Constructive Algebraic Topology: 1. Rolf Schön (Inductive methods). 2. Effective Homology. 3. Operadic Algebraic Topology. Only the second one so far Plan of the talk: 1. Computer illustration led to concrete computer programs. 2. Constructive statement of around CW-complexes. the homological problem. 3. Other computer illustrations. 1
Page 1: Effective Constructive Algebraic To
Page 5 and 6: Notion of CW-Complex X: X = lim −
Page 7 and 8: Example 2. More generally: 1. X0 =
Page 9 and 10: Simplicial version of P ∞ R: P
Page 11 and 12: Easy up to homotopy. Easiest soluti
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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