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arXiv · 2406.14431

Some remarks on a K\"unneth formula for foliated de Rham cohomology

Mélanie Bertelson
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Abstract

The K\"unneth formula is one of the basic tools for computing cohomology. Its validity for foliated cohomology, that is, for the tangential de Rham cohomology of a foliated manifold, is investigated. The main difficulty encountered is the non-Hausdorff nature of the foliated cohomology spaces, forbidding the completion of the tensor product. The results presented here are a K\"unneth formula when both factors have Hausdorff foliated cohomology, a K\"unneth formula when one factor has Hausdorff finite-dimensional foliated cohomology and a counterexample to an alternative version of the K\"unneth formula. The proof of the second result involves a right inverse for the foliated de Rham differential.

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Mélanie Bertelson. 2024-06-20. Some remarks on a K\"unneth formula for foliated de Rham cohomology. https://arxiv.org/abs/2406.14431

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