PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Polishability of some groups of interval and circle diffeomorphisms

Volume 248 / 2020

Michael P. Cohen Fundamenta Mathematicae 248 (2020), 91-109 MSC: 22A05, 26A45, 26A46. DOI: 10.4064/fm605-1-2019 Published online: 7 June 2019


Let $M=I$ or $M=\mathbb {S}^1$ and let $k\geq 1$. We exhibit a new infinite class of Polish groups by showing that each group $\mathop {\rm Diff}\nolimits _+^{k+{\rm AC}}(M)$, consisting of those $C^k$ diffeomorphisms whose $k$th derivative is absolutely continuous, admits a natural Polish group topology which refines the subspace topology inherited from $\mathop {\rm Diff}\nolimits _+^k(M)$. By contrast, the group $\mathop {\rm Diff}\nolimits _+^{1+{\rm BV}}(M)$, consisting of $C^1$ diffeomorphisms whose derivative has bounded variation, admits no Polish group topology whatsoever.


  • Michael P. CohenDepartment of Mathematics and Statistics
    Carleton College
    One North College Street
    Northfield, MN 55057, U.S.A.

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image