Changes between Initial Version and Version 1 of Ticket #29581, comment 93
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 Sep 21, 2021, 8:05:08 PM (13 months ago)
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Ticket #29581, comment 93
initial v1 6 6 > Perhaps that is a bit special. The torus is a little more interesting example. Mainly what I am thinking is if can we compute the Betti numbers without necessarily knowing what the manifold is in advance. 7 7 8 I don't see how that should be possible . Characteristic cohomology classes usually don't tell you anything about the cohomology of your underlying base space. For once, the characteristic cohomology classes usually don't generate the cohomology groups. Moreover, if a characteristic cohomology class has torsion in the ZZcohomology, its corresponding class in the de Rham cohomology vanishes. So you lose a lot of information on the way.8 I don't see how that should be possible with this implementation. Characteristic cohomology classes usually don't tell you anything about the cohomology of your underlying base space. For once, the characteristic cohomology classes usually don't generate the cohomology groups. Moreover, if a characteristic cohomology class has torsion in the ZZcohomology, its corresponding class in the de Rham cohomology vanishes. So you lose a lot of information on the way. 9 9 10 10 > > > Perhaps as a followup ticket, a thematic tutorial on how to compute with the cohomology classes of the manifold might be good (using the modulelevel doc as a starting point).