https://drorbn.net/index.php?action=history&feed=atom&title=Talk%3A0708-1300%2FClass_notes_for_Tuesday%2C_November_13Talk:0708-1300/Class notes for Tuesday, November 13 - Revision history2026-06-19T16:24:51ZRevision history for this page on the wikiMediaWiki 1.39.6https://drorbn.net/index.php?title=Talk:0708-1300/Class_notes_for_Tuesday,_November_13&diff=5949&oldid=prevTrefor at 00:41, 26 November 20072007-11-26T00:41:06Z<p></p>
<p><b>New page</b></p><div>Aptikuis:<br />
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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)<br />
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Hence for <math>\phi:M\rightarrow N</math> we get a pullback (and hence superscript *) map on the differential forms <math>\phi^*:\Omega^p(N)\rightarrow\Omega^p(M)</math> (see Definition 2.6 pg 263 of Bredon)<br />
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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. <br />
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Trefor</div>Trefor