Hodge theory for Riemannian solenoids.
| dc.book.title | Functional Equations in Mathematical Analysis | |
| dc.contributor.author | Muñoz, Vicente | |
| dc.contributor.author | Pérez Marco, Ricardo | |
| dc.contributor.editor | Rassias, Themistocles | |
| dc.contributor.editor | Brzdek, Janusz | |
| dc.date.accessioned | 2023-06-20T05:45:19Z | |
| dc.date.available | 2023-06-20T05:45:19Z | |
| dc.date.issued | 2012 | |
| dc.description | Dedicated to the Memory of the 100th Anniversary of S. M. Ulam | |
| dc.description.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. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | MEC | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/21338 | |
| dc.identifier.doi | 10.1007/978-1-4614-0055-4_39 | |
| dc.identifier.isbn | 978-1-4614-0054-7 | |
| dc.identifier.officialurl | http://link.springer.com/chapter/10.1007%2F978-1-4614-0055-4_39 | |
| dc.identifier.relatedurl | http://link.springer.com | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/45446 | |
| dc.issue.number | 52 | |
| dc.language.iso | eng | |
| dc.page.final | 657 | |
| dc.page.initial | 633 | |
| dc.page.total | 748 | |
| dc.publication.place | Berlin | |
| dc.publisher | Springer | |
| dc.relation.ispartofseries | Springer Optimization and Its Applications | |
| dc.relation.projectID | MTM2007-63582. | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 515.1 | |
| dc.subject.keyword | Solenoids | |
| dc.subject.keyword | Harmonic forms | |
| dc.subject.keyword | Cohomology | |
| dc.subject.keyword | Hodge theory. | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | Hodge theory for Riemannian solenoids. | |
| dc.type | book part | |
| dcterms.references | 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) | |
| dspace.entity.type | Publication |
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