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Diffeomorphism group valued cocycles over higher-rank abelian Anosov actions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2020 (English)In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 40, no 1, p. 117-141Article in journal (Refereed) Published
Abstract [en]

We prove that every smooth diffeomorphism group valued cocycle over certain Z(k) Anosov actions on tori (and more generally on infranilmanifolds) is a smooth coboundary on a finite cover, if the cocycle is center bunched and trivial at a fixed point. For smooth cocycles which are not trivial at a fixed point, we have smooth reduction of cocycles to constant ones, when lifted to the universal cover. These results on cocycle trivialization apply, via the existing global rigidity results, to maximal Cartan Z(k) (k >= 3) actions by Anosov diffeomorphisms (with at least one transitive), on any compact smooth manifold. This is the first rigidity result for cocycles over Z(k) actions with values in diffeomorphism groups which does not require any restrictions on the smallness of the cocycle or on the diffeomorphism group.

Place, publisher, year, edition, pages
CAMBRIDGE UNIV PRESS , 2020. Vol. 40, no 1, p. 117-141
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-266271DOI: 10.1017/etds.2018.22ISI: 000500187000005Scopus ID: 2-s2.0-85045054090OAI: oai:DiVA.org:kth-266271DiVA, id: diva2:1383650
Note

QC 20200108

Available from: 2020-01-08 Created: 2020-01-08 Last updated: 2020-01-08Bibliographically approved

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