De Rham cohomology of the weak stable foliation of the geodesic flow of a hyperbolic surface

Hirokazu Maruhashi; Mitsunobu Tsutaya

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arXiv · 2103.12403

De Rham cohomology of the weak stable foliation of the geodesic flow of a hyperbolic surface

Hirokazu Maruhashi·Mitsunobu Tsutaya

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Abstract

We compute the de Rham cohomology of the weak stable foliation of the geodesic flow of a connected orientable closed hyperbolic surface with various coefficients. For most of the coefficients, we also give certain "Hodge decompositions" of the corresponding de Rham complexes, which are not obtained by the usual Hodge theory of foliations. These results are based on unitary representation theory of $\mathrm{PSL}(2,\mathbb{R})$. As an application we obtain an answer to a problem considered by Haefliger and Li around 1980.

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Hirokazu Maruhashi, Mitsunobu Tsutaya. 2021-03-23. De Rham cohomology of the weak stable foliation of the geodesic flow of a hyperbolic surface. https://arxiv.org/abs/2103.12403

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