Freedman, Michael H.; He, Zheng-Xu A remark on inherent differentiablity. (English) Zbl 0689.57021 Proc. Am. Math. Soc. 104, No. 4, 1305-1310 (1988). Summary: Harrison’s analysis of \(C^ r\)-diffeomorphisms which are not conjugate t \(C^ 8\)-diffeomorphisms for \(s>r>0\) is extended to dimension 4. Also topological conjugacy may be generalized to an arbitrary change of differentiable structure. Combining these statements yields: for any smooth manifold of dimension \(\geq 2\) there is a \(C^ r\)-diffeomorphism which is not a \(C^ 8\)-diffeomorphism with respect to any smooth structure. MSC: 57R50 Differential topological aspects of diffeomorphisms 58C99 Calculus on manifolds; nonlinear operators 57R30 Foliations in differential topology; geometric theory 37-XX Dynamical systems and ergodic theory Keywords:non-conjugate diffeomorphisms; topological conjugacy; smooth manifold PDFBibTeX XMLCite \textit{M. H. Freedman} and \textit{Z.-X. He}, Proc. Am. Math. Soc. 104, No. 4, 1305--1310 (1988; Zbl 0689.57021) Full Text: DOI References: [1] A. Denjoy, Sur les courbes définies par les équations différentielles à la surface du tore, J. Math. Pures Appl. 11 (1932), 333-375. · JFM 58.1124.04 [2] Jenny Harrison, Unsmoothable diffeomorphisms, Ann. of Math. (2) 102 (1975), no. 1, 85 – 94. · Zbl 0316.57018 [3] Jenny Harrison, Unsmoothable diffeomorphisms on higher dimensional manifolds, Proc. Amer. Math. Soc. 73 (1979), no. 2, 249 – 255. · Zbl 0405.57019 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.