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Hodge Theory for Riemannian Solenoids

  • Vicente Muñoz
  • Ricardo Pérez Marco
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 52)

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 

Notes

Acknowledgement

Partially supported through grant MEC (Spain) MTM2007-63582.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Facultad de MatemáticasUniversidad Complutense de MadridMadridSpain
  2. 2.CNRS, LAGA UMR 7539Université Paris XIIIVilletaneuseFrance

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