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Hodge Theory for Riemannian Solenoids

In: Functional Equations in Mathematical Analysis

Author

Listed:
  • Vicente Muñoz

    (Universidad Complutense de Madrid)

  • Ricardo Pérez Marco

    (Université Paris XIII)

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.

Suggested Citation

  • Vicente Muñoz & Ricardo Pérez Marco, 2011. "Hodge Theory for Riemannian Solenoids," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Janusz Brzdek (ed.), Functional Equations in Mathematical Analysis, chapter 0, pages 633-657, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-0055-4_39
    DOI: 10.1007/978-1-4614-0055-4_39
    as

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