Effective Constructive Algebraic Topology - Institut Fourier

Cellular homology.
S n = S 1 × D n−1 / ∼ with (z, x) ∼ (z ′ , x ′ ) if x = x ′ ∈ ∂D n−1 .
D 1 = I
S 1 × 1
S 1 × 0
S 1
∗ × I
• ∗
↦−→
Canonical self-map of degree k for S n :
Theorem (Hopf): C(S n , S n )/∼ ∼ = Z.
•
•
αk : S n → S n : (z, x) ↦→ (z n , x).
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