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Christopher Deninger; Wilhelm Singhof
A counterexample to smooth leafwise Hodge decomposition for general foliations and to a type of dynamical trace formulas
(Un contre-exemple à la décomposition lisse de Hodge pour des feuilletages généraux et à une classe de formules de traces dynami)
Annales de l'institut Fourier, 51 no. 1 (2001), p. 209-219, doi: 10.5802/aif.1821
Article PDF | Reviews MR 1821074 | Zbl 0997.58017
Class. Math.: 53C12, 37C27, 58J60
Keywords: Hodge decomposition, foliation, dynamical trace formula, nilmanifold

Résumé - Abstract

We construct a two dimensional foliation with dense leaves on the Heisenberg nilmanifold for which smooth leafwise Hodge decomposition does not hold. It is also shown that a certain type of dynamical trace formulas relating periodic orbits with traces on leafwise cohomologies does not hold for arbitrary flows.

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