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Hodge theory for Riemannian solenoids.

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Muñoz, Vicente and Pérez Marco, Ricardo (2012) Hodge theory for Riemannian solenoids. In Functional Equations in Mathematical Analysis. Springer Optimization and Its Applications (52). Springer, Berlin, pp. 633-657. ISBN 978-1-4614-0054-7

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Official URL: http://link.springer.com/chapter/10.1007%2F978-1-4614-0055-4_39


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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.


Item Type:Book Section
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Dedicated to the Memory of the 100th Anniversary of S. M. Ulam

Uncontrolled Keywords:Solenoids; Harmonic forms; Cohomology; Hodge theory.
Subjects:Sciences > Mathematics > Topology
ID Code:21338
Deposited On:13 May 2013 12:37
Last Modified:12 Dec 2018 15:13

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