Timeline for Torsion in cohomology of smooth manifolds
Current License: CC BY-SA 3.0
3 events
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| Dec 19, 2012 at 23:34 | comment | added | Liviu Nicolaescu | Yes, that is true. But the middle Betti number in dimensions divisible by $4$ can be odd. Take for example the cade of complex projective spaces of even complex dimensions. That is why Serre's observation is so strange. He has other examples, and all have to do with the numerators of Bernoulli numbers. | |
| Dec 19, 2012 at 23:01 | comment | added | Will Sawin | More trivially, if the dimension is $2$ mod $4$, then the middle cohomology of a manifold is even-dimensional, because Poincare duality provides a nondegenerate symplectic bilinear form. | |
| Dec 19, 2012 at 20:50 | history | answered | Liviu Nicolaescu | CC BY-SA 3.0 |