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Hatcher-Algebraic-Topology
· Problem 25
Homotopy Theory
Mathematics — Graph Theory · hurewicz-map-quotient
Problem
For
X
X
X
a connected CW complex with
π
i
(
X
)
=
0
\pi_i(X) = 0
π
i
(
X
)
=
0
for
1
<
i
<
n
1 < i < n
1
<
i
<
n
for some
n
≥
2
n \geq 2
n
≥
2
, show that
H
n
(
X
)
/
h
(
π
n
(
X
)
)
≈
H
n
(
K
(
π
1
(
X
)
,
1
)
)
H_n(X)/h(\pi_n(X)) \approx H_n\bigl(K(\pi_1(X), 1)\bigr)
H
n
(
X
)
/
h
(
π
n
(
X
))
≈
H
n
(
K
(
π
1
(
X
)
,
1
)
)
, where
h
h
h
is the Hurewicz map.
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