Homework number 2
Do two from the following three exercises.
Exercise 4. Prove surjectivity in 5-lemma.
Exercise 5. Let X be a topological space and x a point not in X. Compute H∗(X ⊔
{x}, {x}) using H∗(X).
Exercise 6. Compute the homology groups if you know that the following sequence
of homomorphisms is a chain complex
0 → C5 = Z
f
−→ C4 = Z → C3 = Z
0
−→ C2 = Z ⊕ Z
g
−→ C1 = Z ⊕ Z ⊕ Z
0
−→ C0 = Z → 0
and f(a) = 3a and g(b, c) = (b + c, b − c, c − b).
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