A remark on inherent differentiability
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- by Michael H. Freedman and Zheng-Xu He PDF
- Proc. Amer. Math. Soc. 104 (1988), 1305-1310 Request permission
Abstract:
Harrison’s analysis of ${C^r}$-diffeomorphisms which are not conjugate to ${C^s}$-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 ${C^s}$-diffeomorphism w.r.t. any smooth structure.References
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A. Denjoy, Sur les courbes définies par les équations différentielles à la surface du tore, J. Math. Pures Appl. 11 (1932), 333-375.
- Jenny Harrison, Unsmoothable diffeomorphisms, Ann. of Math. (2) 102 (1975), no. 1, 85–94. MR 388458, DOI 10.2307/1970975
- Jenny Harrison, Unsmoothable diffeomorphisms on higher dimensional manifolds, Proc. Amer. Math. Soc. 73 (1979), no. 2, 249–255. MR 516473, DOI 10.1090/S0002-9939-1979-0516473-9
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 1305-1310
- MSC: Primary 57R50; Secondary 58F99
- DOI: https://doi.org/10.1090/S0002-9939-1988-0937012-X
- MathSciNet review: 937012