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Hatcher-Algebraic-Topology
· Problem 4.1.3
Homotopy Theory
Mathematics — Graph Theory · h-spaces-homotopy-groups
Problem
For an H--space
(
X
,
x
0
)
(X, x_0)
(
X
,
x
0
)
with multiplication
μ
:
X
×
X
→
X
\mu : X \times X \to X
μ
:
X
×
X
→
X
, show that the group operation in
π
n
(
X
,
x
0
)
\pi_n(X, x_0)
π
n
(
X
,
x
0
)
can also be defined by the rule
(
f
+
g
)
(
x
)
=
μ
(
f
(
x
)
,
g
(
x
)
)
(f + g)(x) = \mu\bigl(f(x), g(x)\bigr)
(
f
+
g
)
(
x
)
=
μ
(
f
(
x
)
,
g
(
x
)
)
.
Related theory
Higher Homotopy Groups And The Hurewicz Theorem
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