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Hatcher-Algebraic-Topology
· Problem 3F.8
Cohomology
Mathematics — Graph Theory · limits-and-ext
Problem
Show that for a Moore space
M
(
G
,
n
)
M(G, n)
M
(
G
,
n
)
the Bockstein long exact sequence in cohomology associated to the short exact sequence of coefficient groups
0
→
A
→
B
→
C
→
0
0 \to A \to B \to C \to 0
0
→
A
→
B
→
C
→
0
reduces to an exact sequence
0
→
H
o
m
(
G
,
A
)
→
H
o
m
(
G
,
B
)
→
H
o
m
(
G
,
C
)
→
E
x
t
(
G
,
A
)
→
E
x
t
(
G
,
B
)
→
E
x
t
(
G
,
C
)
→
0
0 \to \mathrm{Hom}(G, A) \to \mathrm{Hom}(G, B) \to \mathrm{Hom}(G, C) \to \mathrm{Ext}(G, A) \to \mathrm{Ext}(G, B) \to \mathrm{Ext}(G, C) \to 0
0
→
Hom
(
G
,
A
)
→
Hom
(
G
,
B
)
→
Hom
(
G
,
C
)
→
Ext
(
G
,
A
)
→
Ext
(
G
,
B
)
→
Ext
(
G
,
C
)
→
0
Related theory
Infinite Limits And Limits At Infinity
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