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1. • CommentRowNumber1.
   • CommentAuthorjoe.hannon
   • CommentTimeDec 14th 2014
   • PermaLink
   Author: joe.hannon
   Format: MarkdownItexIn [transgression](http://ncatlab.org:8080/nlab/show/transgression) it states that for a fibration $F\overset{i}{\to} P\overset{p}{\to} X$, an element $\omega \in H^n_\text{dR}(F)$ is transgressive if there exists $\text{cs}\in\Omega^n(P)$ such that $i^*\text{cs}=\omega$ and $d\omega=p^*\kappa$ for $\kappa\in\Omega^{n+1}(X).$ Is this right? It doesn't seem to make sense, since the pullback of a form on the base $X$ should give a form on the total space $P$. Maybe it is supposed to say $d(\text{cs})=p^*\kappa$? I checked the cited source by Borel, and the sentence is ambiguous there.

   In transgression it states that for a fibration $F\overset{i}{\to} P\overset{p}{\to} X$, an element $\omega \in H^n_\text{dR}(F)$ is transgressive if there exists $\text{cs}\in\Omega^n(P)$ such that $i^*\text{cs}=\omega$ and $d\omega=p^*\kappa$ for $\kappa\in\Omega^{n+1}(X).$

   Is this right? It doesn’t seem to make sense, since the pullback of a form on the base $X$ should give a form on the total space $P$. Maybe it is supposed to say $d(\text{cs})=p^*\kappa$? I checked the cited source by Borel, and the sentence is ambiguous there.

2. • CommentRowNumber2.
   • CommentAuthorjoe.hannon
   • CommentTimeDec 14th 2014
   • PermaLink
   Author: joe.hannon
   Format: MarkdownItexProposition 18.13 of Bott and Tu agrees that transgression is defined in the sensible way. I edited the article. Thanks.

   Proposition 18.13 of Bott and Tu agrees that transgression is defined in the sensible way. I edited the article. Thanks.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeDec 14th 2014
   • (edited Dec 14th 2014)
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   Author: Urs
   Format: MarkdownItexYes, $d cs$ of course, this was a typo. Thanks for catching and fixing it.

   Yes, $d cs$ of course, this was a typo. Thanks for catching and fixing it.