Publication:
Hodge theory for Riemannian solenoids.

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http://link.springer.com/chapter/10.1007%2F978-1-4614-0055-4_39
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2012
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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.
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Dedicated to the Memory of the 100th Anniversary of S. M. Ulam
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Topología
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1210 Topología
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Dodziuk, J.: Sobolev spaces of differential forms and De Rham-Hodge isomorphism. J. Diff. Geom. 16, 63–73 (1981) Heitsch, J.L.: A cohomology of foliated manifolds. Comment. Math. Helvetici 50, 197–218 (1975) Macias, E.: Continuous cohomology of linear foliations on T 2. Rediconti di Matematica Serie VII (Roma) 11, 523–528 (1991) Massey, W.S.: Singular Homology Theory. Graduate Texts in Mathematics 70, Springer-Verlag (1980) Moore, C., Schochet, C.: Global analysis on foliated spaces. Mathematical Sciences Research Institute Publications 9, Springer-Verlag (1988) Muñoz, V., Pérez-Marco, R.: Ergodic solenoids and generalized currents. Preprint. Muñoz, V., Pérez-Marco, R.: Schwartzman cycles and ergodic solenoids. Preprint. Muñoz, V., Pérez-Marco, R.: Ergodic solenoidal homology: Realization theorem. Preprint. Muñoz, V., Pérez-Marco, R.: Ergodic solenoidal homology II: Density of ergodic solenoids. Aust. J. Math. Anal. Appl. 6, no. 1, Article 11, 1–8 (2009) Reinhart, B.L.: Harmonic integrals on almost product manifolds. Trans. Amer. Math. Soc. 88, 243–276 (1958) Ruelle, D., Sullivan, D.: Currents, flows and diffeomorphisms. Topology 14, 319–327 (1975) Wells, R.O.: Differential analysis on complex manifolds. GTM 65, Second Edition, Springer-Verlag (1979)
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https://hdl.handle.net/20.500.14352/45446
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