On Rumin's Complex and Adiabatic Limits

Details On Rumin's Complex and Adiabatic Limits On Rumin's Complex and Adiabatic Limits

1994-10-05

arxiv.org/abs/dg-ga/9410003v1

Mathematics

Differential Geometry

18 pages

Scientific paper

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 $L^2$-norms will converge to Rumin's harmonic forms. This proves a conjecture in Gromov `` Carnot-Caratheodory spaces seen from within '', IHES preprint, 1994. 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.

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