Next Article in Journal
Skew Continuous Morphisms of Ordered Lattice Ringoids
Previous Article in Journal
New Method of Randomized Forecasting Using Entropy-Robust Estimation: Application to the World Population Prediction
Previous Article in Special Issue
Multiplicative Expression for the Coefficient in Fermionic 3–3 Relation
Article Menu

Export Article

Open AccessArticle
Mathematics 2016, 4(1), 18;

Dynamics and the Cohomology of Measured Laminations

Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro 21941-909, Brazil
Academic Editor: Yuli B. Rudyak
Received: 28 November 2015 / Revised: 19 February 2016 / Accepted: 4 March 2016 / Published: 15 March 2016
(This article belongs to the Special Issue Algebraic and Geometric Topology)
Full-Text   |   PDF [556 KB, uploaded 15 March 2016]   |  


In this paper, the interconnection between the cohomology of measured group actions and the cohomology of measured laminations is explored, the latter being a generalization of the former for the case of discrete group actions and cocycles evaluated on abelian groups. This relation gives a rich interplay between these concepts. Several results can be adapted to this setting—for instance, Zimmer’s reduction of the coefficient group of bounded cocycles or Fustenberg’s cohomological obstruction for extending the ergodicity \(\mathbb{Z}\)-action to a skew product relative to an \(S^{1}\) evaluated cocycle. Another way to think about foliated cocycles is also shown, and a particular application is the characterization of the existence of certain classes of invariant measures for smooth foliations in terms of the \(L^{\infty}\)-cohomology class of the infinitesimal holonomy. View Full-Text
Keywords: foliations; cohomology; group action; foliated cocycles; invariant measures foliations; cohomology; group action; foliated cocycles; invariant measures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Meniño Cotón, C. Dynamics and the Cohomology of Measured Laminations. Mathematics 2016, 4, 18.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top