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Whitney product formula for Stiefel–Whitney classes
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Geometry and topology
Algebraic topology
Fiber bundle
Vector bundle
Stiefel–Whitney class
Splitting principle for real vector bundles
2026-09-28
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For real
vector bundles
E
and
F
,
w
(
E
⊕
F
)
=
w
(
E
)
w
(
F
)
,
w
k
(
E
⊕
F
)
=
∑
i
+
j
=
k
w
i
(
E
)
w
j
(
F
)
.
(1)
After applying the
splitting principle for real vector bundles
, both sides are the product of
1
+
w
1
(
L
)
over all line summands.
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Splitting principle for real vector bundles
Stiefel–Whitney class
Vector bundle
Fiber bundle
Algebraic topology
Geometry and topology
Area of mathematics
Mathematics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2023
/
iii
/
Paper 142
/
1
/
Solution
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