Effective Constructive Algebraic Topology - Institut Fourier
Effective Constructive Algebraic Topology - Institut Fourier
Effective Constructive Algebraic Topology - Institut Fourier
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Simplicial version of P ∞ R:<br />
P ∞ R = X = K(Z2, 1)<br />
⇒ X ND<br />
n<br />
= {σn}<br />
⇒ C∗X = {· · · ←− 0<br />
Z 0<br />
∂iσn = σn−1 if i = 0, n;<br />
= ηi−1σn−2 if 0 < i < n.<br />
←− 1<br />
Z ×2<br />
←− 2<br />
Z 0<br />
←− 3<br />
Z ×2<br />
←− 4<br />
Z 0<br />
←− 5<br />
Z ×2<br />
⇒ Hi(P ∞ R) = Z if i = 0;<br />
Z2 if i > 0 odd;<br />
0 if i > 0 even.<br />
←− · · ·}<br />
7
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