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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

## 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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Additional Information: | 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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