Complutense University Library

Ergodic Solenoidal Homology: Realization Theorem.


Muñoz, Vicente and Pérez Marco, Ricardo (2011) Ergodic Solenoidal Homology: Realization Theorem. Communications in Mathematical Physics, 302 (3). pp. 737-753. ISSN 0010-3616

[img] PDF
Restringido a Repository staff only hasta 2020.


Official URL:


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.

Item Type:Article
Uncontrolled Keywords:Solenoid; homology; rRealisation; Geometric current
Subjects:Sciences > Mathematics > Topology
ID Code:16961

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, 2010

Muñoz,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 press

Muñoz, 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)

Deposited On:05 Nov 2012 11:24
Last Modified:07 Feb 2014 09:39

Repository Staff Only: item control page