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arXiv · 1307.0518

Diagonal approximation and the cohomology ring of torus fiber bundles

Sérgio Tadao Martins
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Abstract

For a torus bundle (S^1 x S^1) -> E -> S^1$, we construct a finite free resolution Z over ZG, where G is the fundamental group of the total space E, and then we compute the cohomology groups H^*(G,Z) and H^*(G,Z_p) for a prime p. We also construct a partial diagonal approximation for the resolution, which allows us to compute the cup product in H^*(G,Z) and H^*(G,Z_p).

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Sérgio Tadao Martins. 2013-07-01. Diagonal approximation and the cohomology ring of torus fiber bundles. https://arxiv.org/abs/1307.0518

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