RT Journal Article T1 Ergodic Solenoidal Homology: Realization Theorem. A1 Muñoz, Vicente A1 Pérez Marco, Ricardo AB We define generalized currents associated with immersions of abstract oriented solenoids with a transversal measure. We realize geometrically the full real homology of a compact manifold with these generalized currents, and more precisely with immersions of minimal uniquely ergodic solenoids. This makes precise and geometric De Rham's realization of the real homology by only using a restricted geometric subclass of currents. PB Springer SN 0010-3616 YR 2011 FD 2011 LK https://hdl.handle.net/20.500.14352/42378 UL https://hdl.handle.net/20.500.14352/42378 LA eng NO Denjoy, A.: Sur les courbes définies par les équations différentielles à la surface du tore. J. Math. Pures Et Appliquées 11(9. série), 333–375 (1932)Herman, M.R.: Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. Inst.Hautes Études Sci. Publ. Math. 49, 5–233 (1979)Hurder, S., Mitsumatsu, Y.: The intersection product of transverse invariant measures. Indiana Univ.Math. J 40(4), 1169–1183 (1991)Muñoz, V., Pérez-Marco, R.: Ergodic solenoids and generalized currents. Revista Matematica Complutense.In press, doi:10.1007/s13163-010-0050-7, 2010Muñoz,V., Pérez-Marco, R.: Schwartzman cycles and ergodic solenoids. In:Essays inMathematics and its Applications. Dedicated to Stephen Smale, eds. P. Pardalos, Th.M.Rassias. Berlin-Heidelberg-Newyork:Springer. In pressMuñoz, V., Pérez-Marco, R.: Ergodic solenoidal homology: Density of ergodic solenoids. Australian J.Math. Anal. Appl. 6(1), Article 11, 1–8 (2009)Rourke, C., Sanderson, B.: The compression theorem.Geometry & Topology 5, 399–429 (2001)Ruelle, D., Sullivan, D.: Currents, flows and diffeomorphisms. Topology 14(4), 319–327 (1975)Schwartzman, S.: Asymptotic cycles. Ann. Math. 66(2), 270–284 (1957)Serre, J.-P.: Groupes d’homotopie et classes de groupes abéliens.. Ann. Math. 58(2), 258–294 (1943)Sullivan, D.: Cycles for the dynamical study of foliated manifolds and complex manifolds. Invent.Math. 36, 225–255 (1976)Sullivan, D.: René Thom’s work on geometric homology class and bordism. Bull. AMS 41(3), 341–350 (2004)Thom, R.: Sous-variétés et classes d’homologie des variétés différentiables. I et II. C. R. Acad. Sci. Paris 236, 453–454 and 573–575 (1953)Thom, R.: Quelques propriétés globales des variétés différentiables. Commentarii Mathematici Halvetici 236, 17–86 (1954)Wells, R.: Cobordisms groups of immersions. Topology 5, 281–294 (1966)Zucker, S.: The Hodge conjecture for cubic fourfolds. Compositio. Math. 34, 199–209 (1977) NO MEC NO CNRS DS Docta Complutense RD 16 may 2024