Talk:0708-1300/Class notes for Tuesday, November 13

Aptikuis:

I changed back your edit regarding the pullback of differential forms. I could be wrong but it is my understanding that forms pull back and we use superscript * for the pullback (such as for functions) vs the subscript * we use for pushforwards (such as of tangent vectors or points)

Hence for $\phi :M\rightarrow N$ we get a pullback (and hence superscript *) map on the differential forms $\phi ^{*}:\Omega ^{p}(N)\rightarrow \Omega ^{p}(M)$ (see Definition 2.6 pg 263 of Bredon)

However, as originally typed in the notes, the pullback of forms is defined in terms of the pushforward of tangent vectors which comes with the subscript.

Trefor