Effective Constructive Algebraic Topology - Institut Fourier

Translation: No known algorithm using these methods
computes H∗(Ω n X) for n ≥ 3
except when X is an n-suspension X = Σ n Y .
Typical example: H∗(Ω 3 (P ∞ R/P 3 R)) = ???
Adams: There exists a finite-type CW-complex
with the homotopy type of Ω 3 (P ∞ R/P 3 R).
Dimension 0 1 2 3 4 5 6 7 8 9 10 · · ·
Cell-# 1 1 2 5 13 33 84 214 545 1388 3535 · · ·
But what about the homological boundary matrices ???
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