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Algebraic Topology
· Problem 2.2.27
Homology — Allen Hatcher
Mathematics — Topology · split-exact-sequences
Problem
The short exact sequences
0
→
C
n
(
A
)
→
C
n
(
X
)
→
C
n
(
X
,
A
)
→
0
0 \to C_n(A) \to C_n(X) \to C_n(X, A) \to 0
0
→
C
n
(
A
)
→
C
n
(
X
)
→
C
n
(
X
,
A
)
→
0
always split, but why does this not always yield splittings
H
n
(
X
)
≈
H
n
(
A
)
⊕
H
n
(
X
,
A
)
H_n(X) \approx H_n(A) \oplus H_n(X, A)
H
n
(
X
)
≈
H
n
(
A
)
⊕
H
n
(
X
,
A
)
?
Related theory
Sequences Convergence Cauchy Sequences Subsequences
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