Foliated de Rham Cohomology - Fiberwise Exact Implies Exact?
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Let $F:X to Y$ be a surjective submersion between smooth manifolds. Consider the induced foliated de Rham cohomology on $X$. Is it true that if a closed form is leafwise exact, then it is exact in foliated cohomology? If not, are there other conditions that will ensure a leafwise exact form is exact? I'm fine with assuming the submersion has a section, and maybe some connectedness assumptions of the leaves. References would be appreciated.
smooth-manifolds de-rham-cohomology foliations
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Let $F:X to Y$ be a surjective submersion between smooth manifolds. Consider the induced foliated de Rham cohomology on $X$. Is it true that if a closed form is leafwise exact, then it is exact in foliated cohomology? If not, are there other conditions that will ensure a leafwise exact form is exact? I'm fine with assuming the submersion has a section, and maybe some connectedness assumptions of the leaves. References would be appreciated.
smooth-manifolds de-rham-cohomology foliations
asked yesterday
JLA
4,39911427
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Let $F:X to Y$ be a surjective submersion between smooth manifolds. Consider the induced foliated de Rham cohomology on $X$. Is it true that if a closed form is leafwise exact, then it is exact in foliated cohomology? If not, are there other conditions that will ensure a leafwise exact form is exact? I'm fine with assuming the submersion has a section, and maybe some connectedness assumptions of the leaves. References would be appreciated.
smooth-manifolds de-rham-cohomology foliations
asked yesterday
JLA
4,39911427
Let $F:X to Y$ be a surjective submersion between smooth manifolds. Consider the induced foliated de Rham cohomology on $X$. Is it true that if a closed form is leafwise exact, then it is exact in foliated cohomology? If not, are there other conditions that will ensure a leafwise exact form is exact? I'm fine with assuming the submersion has a section, and maybe some connectedness assumptions of the leaves. References would be appreciated.
smooth-manifolds de-rham-cohomology foliations
smooth-manifolds de-rham-cohomology foliations
asked yesterday
JLA
4,39911427
asked yesterday
JLA
4,39911427
asked yesterday
JLA
4,39911427
asked yesterday
JLA
4,39911427
asked yesterday
JLA
4,39911427
4,39911427
add a comment |
add a comment |
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