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Homotopy theory, homological algebra, algebraic treatments of manifolds.
8
votes
2
answers
1k
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Künneth theorem for fibred products
Given the fibred product of two manifolds over a base space $X\times_Y Z$ , is there an analogue of Künneth theorem that allows one to compute the cohomology of the fibred product?
1
vote
1
answer
529
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group extensions and principal bundles
Given an extension of groups, say
$$0 \to H \stackrel{i}{\to} G \stackrel{q}{\to} G/H \to 0$$
and a $H$-principal fiber bundle $P \to X$, one can use induction to obtain bundles with fibers $G$ and $ …