Poincare lemma or it's converse?
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In the old days the name "Poincare lemma" used to be the statement that $d^2=0$. This is the usage of of books like Flanders' "Differential Forms with Applications to the Physical Sciences ", Bishop and Goldberg's "Tensor Analysis on Manifolds" and more recently (2014) Weintraub's "Differential Forms: Theory and practice". Today many authors seem to us the name "Poincare lemma" to refer to the partial converse i.e to the exactness of closed forms on retractable spaces. This theorem to be called the "converse of the Poincare lemma" Does anyone know how this change of usage came about?
differential-topology
asked Jan 23 at 16:29
mike stonemike stone
34317
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add a comment |
$begingroup$
In the old days the name "Poincare lemma" used to be the statement that $d^2=0$. This is the usage of of books like Flanders' "Differential Forms with Applications to the Physical Sciences ", Bishop and Goldberg's "Tensor Analysis on Manifolds" and more recently (2014) Weintraub's "Differential Forms: Theory and practice". Today many authors seem to us the name "Poincare lemma" to refer to the partial converse i.e to the exactness of closed forms on retractable spaces. This theorem to be called the "converse of the Poincare lemma" Does anyone know how this change of usage came about?
differential-topology
asked Jan 23 at 16:29
mike stonemike stone
34317
$endgroup$
1
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Great question. I found the later usage of Poincaré Lemma in my copy of Spivak's Comprehensive Introduction to Differential Geometry (1970)
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– Matthew Leingang
Jan 23 at 16:34
add a comment |
$begingroup$
In the old days the name "Poincare lemma" used to be the statement that $d^2=0$. This is the usage of of books like Flanders' "Differential Forms with Applications to the Physical Sciences ", Bishop and Goldberg's "Tensor Analysis on Manifolds" and more recently (2014) Weintraub's "Differential Forms: Theory and practice". Today many authors seem to us the name "Poincare lemma" to refer to the partial converse i.e to the exactness of closed forms on retractable spaces. This theorem to be called the "converse of the Poincare lemma" Does anyone know how this change of usage came about?
differential-topology
asked Jan 23 at 16:29
mike stonemike stone
34317
$endgroup$
In the old days the name "Poincare lemma" used to be the statement that $d^2=0$. This is the usage of of books like Flanders' "Differential Forms with Applications to the Physical Sciences ", Bishop and Goldberg's "Tensor Analysis on Manifolds" and more recently (2014) Weintraub's "Differential Forms: Theory and practice". Today many authors seem to us the name "Poincare lemma" to refer to the partial converse i.e to the exactness of closed forms on retractable spaces. This theorem to be called the "converse of the Poincare lemma" Does anyone know how this change of usage came about?
differential-topology
differential-topology
asked Jan 23 at 16:29
mike stonemike stone
34317
asked Jan 23 at 16:29
mike stonemike stone
34317
asked Jan 23 at 16:29
mike stonemike stone
34317
asked Jan 23 at 16:29
mike stonemike stone
34317
asked Jan 23 at 16:29
mike stonemike stone
34317
34317
1
$begingroup$
Great question. I found the later usage of Poincaré Lemma in my copy of Spivak's Comprehensive Introduction to Differential Geometry (1970)
$endgroup$
– Matthew Leingang
Jan 23 at 16:34
add a comment |
1
$begingroup$
Great question. I found the later usage of Poincaré Lemma in my copy of Spivak's Comprehensive Introduction to Differential Geometry (1970)
$endgroup$
– Matthew Leingang
Jan 23 at 16:34
1
1
$begingroup$
Great question. I found the later usage of Poincaré Lemma in my copy of Spivak's Comprehensive Introduction to Differential Geometry (1970)
$endgroup$
– Matthew Leingang
Jan 23 at 16:34
$begingroup$
Great question. I found the later usage of Poincaré Lemma in my copy of Spivak's Comprehensive Introduction to Differential Geometry (1970)
$endgroup$
– Matthew Leingang
Jan 23 at 16:34
add a comment |
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Great question. I found the later usage of Poincaré Lemma in my copy of Spivak's Comprehensive Introduction to Differential Geometry (1970)
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– Matthew Leingang
Jan 23 at 16:34