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Mayer--Vietoris sequence for de Rham cohomology
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Geometry and topology
Differential form
Exterior derivative
Closed differential form
Exact differential form
de Rham cohomology
2026-09-28
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For an
open cover
X
=
U
∪
V
, restriction of forms gives
a
short exact sequence
of
cochain complexes
0
→
Ω
∗
(
X
)
→
Ω
∗
(
U
)
⊕
Ω
∗
(
V
)
→
Ω
∗
(
U
∩
V
)
→
0
,
(1)
and hence
a
long
exact sequence
in
de Rham cohomology
.
Ancestors
(9)
de Rham cohomology
Exact differential form
Closed differential form
Exterior derivative
Differential form
Geometry and topology
Area of mathematics
Mathematics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2005
/
iii
/
Paper 15
/
1
/
Solution
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