Publication: Schwartzman cycles and ergodic solenoids.
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Publication Date
2012
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Springer-Verlag
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Abstract
We extend Schwartzman theory beyond dimension 1 and provide a unified treatment of Ruelle-Sullivan and Schwartzman theories via Birkhoff’s ergodic theorem for the class
of immersions of solenoids with a trapping region.
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V. Muñoz, R. Perez-Marco, Intersection theory for ergodic solenoids (2009). Arxiv preprint arXiv:0910.2915
V. Muñoz, R. Pérez-Marco, Ergodic solenoidal homology: realization theorem. Commun. Math. Phys. 302, 737–753 (2011)
V. Munoz, R. P. Marco, Hodge theory for Riemannian solenoids. Funct. Equ. Math. Anal. 633–657 (2012). Springer
D. Ruelle, D. Sullivan, Currents, flows and diffeomorphisms. Topology 14, 319–327 (1975)
S. Schwartzman, Asymptotic cycles. Ann. Math. 66(2), 270–284 (1957)
R. Thom, Sous-variétés et classes d’homologie des variétés différentiables. I et II. C. R. Acad. Sci. Paris 236, 453–454, 573–575 (1953)