On Adiabatic Limits and Rumin’s Complex
نویسنده
چکیده
This paper shows that when the Riemannian metric on a contact manifold is blown up along the direction orthogonal to the contact distribution, the corresponding harmonic forms rescaled and normalized in the L2-norms will converge to Rumin’s harmonic forms. This proves a conjecture in Gromov [11]. This result can also be reformulated in terms of spectral sequences, after Forman, Mazzeo-Melrose. A key ingredient in the proof is the fact that the curvatures become unbounded in a controlled way. ∗Supported by the Ministry of Colleges and Universities of Ontario and the Natural Sciences and Engineering Research Council of Canada
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