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Hodge Theory for Riemannian Solenoids

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Functional Equations in Mathematical Analysis

Part of the book series: Springer Optimization and Its Applications ((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.

Mathematics SubjectClassification (2000): Primary 58A14; Secondary 57R30, 58A12

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Acknowledgement

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

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Authors and Affiliations

  1. Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza Ciencias 3, 28040, Madrid, Spain

    Vicente Muñoz

  2. CNRS, LAGA UMR 7539, Université Paris XIII, 99, Avenue J.-B. Clément, 93430, Villetaneuse, France

    Ricardo Pérez Marco

Authors
  1. Vicente Muñoz
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  2. Ricardo Pérez Marco
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Corresponding author

Correspondence to Vicente Muñoz .

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Editors and Affiliations

  1. , Department of Mathematics, National Technical University of Athens, Iroon Polytechneiou 9, Athens, 15780, Greece

    Themistocles M. Rassias

  2. Institute of Mathematics, Pedagogical University, ul. Podchorazych 2, Krakow, 30-084, Poland

    Janusz Brzdek

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Muñoz, V., Marco, R.P. (2011). Hodge Theory for Riemannian Solenoids. In: Rassias, T., Brzdek, J. (eds) Functional Equations in Mathematical Analysis. Springer Optimization and Its Applications(), vol 52. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0055-4_39

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