Hodge theory for Riemannian solenoids.



Downloads per month over past year

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

[thumbnail of VMuñoz71.pdf]

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


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
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

Origin of downloads

Repository Staff Only: item control page