I read a problem a while ago which was to find a differential form on the circle which is not the differential of any function. Being a hapless physicist, this puzzled me for a while. I've found an answer in Spivak's Calculus on Manifolds, but I need a little help in following his reasoning.(adsbygoogle = window.adsbygoogle || []).push({});

He argues that the form [tex]d\theta[/tex] is such a form, and shows that if it is the differential of a function [tex]f[/tex] then [tex]f = \theta + constant[/tex]. I am OK up to this point, but I fail to see how such an [tex]f[/tex] can't exist, like he argues.

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# Forms on the circle

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