The Diffeomorphism Group of a Lie Foliation
نویسندگان
چکیده
We explicitly compute the diffeomorphism group of several types of linear foliations (with dense leaves) on the torus T, n ≥ 2, namely codimension one foliations, flows, and the so-called nonquadratic foliations. We show in particular that non-quadratic foliations are rigid, in the sense that they do not admit transverse diffeomorphisms other than ±id and translations. The computation is an application of a general formula that we prove for the diffeomorphism group of any Lie foliation with dense leaves on a compact manifold. Our results generalize those of P. Donato and P. Iglesias for T , P. Iglesias and G. Lachaud for codimension one foliations on T, n ≥ 2, and B. Herrera for transcendent foliations. The theoretical setting of the paper is that of J. M. Souriau’s diffeological spaces.
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