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Hatcher-Algebraic-Topology
· Problem 2.2.15
Homology
Mathematics — Graph Theory · cellular-homology
Problem
Show that if
X
X
X
is a CW complex then
H
n
(
X
n
)
H_n(X^n)
H
n
(
X
n
)
is free by identifying it with the kernel of the cellular boundary map
H
n
(
X
n
,
X
n
−
1
)
→
H
n
−
1
(
X
n
−
1
,
X
n
−
2
)
H_n(X^n, X^{n-1}) \to H_{n-1}(X^{n-1}, X^{n-2})
H
n
(
X
n
,
X
n
−
1
)
→
H
n
−
1
(
X
n
−
1
,
X
n
−
2
)
.
Related theory
Cw Complexes And Cellular Homology
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