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Homotopy theory, homological algebra, algebraic treatments of manifolds.

10 votes

Open Torelli problems

There are versions of the Global Torelli Problem for Calabi-Yau threefolds which are open. Infinitesimal Torelli is true for CY3s, i.e. (families of) projective 3-folds with trivial canonical bundle a …
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4 votes

Kunneth formular with coefficients the constructible sheaves

Theorem 4.3.14 in Dimca's Sheaves and topology says this is true. The compact version, Corollary 2.3.31, is indeed much easier as you suggest. Another reference Dimca gives is Schuermann's Topology of …
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