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16 votes

Poincare duality on the level of complexes

One way of finding a "fully derived" version of Poincaré duality is Atiyah duality. This says that for any closed manifold $M$ there is an equivalence of spectra (in the sense of algebraic topology) $ …
Denis Nardin's user avatar
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19 votes
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Why Cech cohomology does not compute sheaf cohomology on an open annulus

Functions $(f_0,f_1,f_2)$ as you requested do in fact exist. Your confusion comes from the fact that you are trying to impose the cocycle condition on the intersection $U_0\cap U_1\cap U_2$, which is …
Denis Nardin's user avatar
  • 16.5k