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Algebraic Topology
· Problem 2.1.21
Homology — Allen Hatcher
Mathematics — Topology · suspension-homology
Problem
Making the preceding problem more concrete, construct explicit chain maps
s
:
C
n
(
X
)
→
C
n
+
1
(
S
X
)
s: C_n(X) \to C_{n+1}(SX)
s
:
C
n
(
X
)
→
C
n
+
1
(
S
X
)
inducing isomorphisms
H
~
n
(
X
)
→
H
~
n
+
1
(
S
X
)
\widetilde{H}_n(X) \to \widetilde{H}_{n+1}(SX)
H
n
(
X
)
→
H
n
+
1
(
S
X
)
.
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