Hodge Theory for Riemannian Solenoids

Vicente Muñoz () and Ricardo Pérez Marco ()
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Vicente Muñoz: Universidad Complutense de Madrid
Ricardo Pérez Marco: Université Paris XIII

Chapter Chapter 39 in Functional Equations in Mathematical Analysis, 2011, pp 633-657 from Springer

Abstract: Abstract 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.

Keywords: Solenoids; Harmonic forms; Cohomology; Hodge theory (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-1-4614-0055-4_39

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