Hodge Theory for Riemannian Solenoids
A measured solenoid is a compact laminated space endowed with a transversal measure. The De Rham L 2-cohomology of the solenoid is defined by using differential forms which are smooth in the leafwise directions and L 2 in the transversal direction. We develop the theory of harmonic forms for Riemannian measured solenoids, and prove that this computes the De Rham L 2-cohomology of the solenoid.This implies in particular a Poincaré duality result.
KeywordsSolenoids Harmonic forms Cohomology Hodge theory
Partially supported through grant MEC (Spain) MTM2007-63582.
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