Hodge theory for Riemannian solenoids

Details Hodge theory for Riemannian solenoids Hodge theory for Riemannian solenoids

2010-04-23

arxiv.org/abs/1004.4120v1

Mathematics

Differential Geometry

24 pages

Scientific paper

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 Poincare duality result.

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