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hallo,

let $M$ be a Riemannian manifold (with say metric $g$) with boundary. is then the de Rahm cohomology $H_{dR}^{n}(M)$ one dimensional, where $n$ is the dimension of $M$ ?

pascal

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De Rham cohomology is not a metric object! – diverietti Mar 21 2012 at 8:24
yes, I know. I think I put too much data. But just ignore the metric. is it one dimensional ? – pascal Mar 21 2012 at 8:39
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 Have you tried an example? Like a 1-dimensional manifold with boundary? In other words, a bounded closed interval. – Deane Yang Mar 21 2012 at 8:48
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 It is one-dimensional? What's an example of a closed 1-form on the interval that is not exact? – Deane Yang Mar 21 2012 at 9:14
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 yes well youre right, its zero dimensional. – pascal Mar 21 2012 at 9:20
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closed as too localized by Dan Petersen, Ryan Budney, Deane Yang, Yemon Choi, Chris Godsil Mar 21 2012 at 13:16

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