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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A remark on inherent differentiability

Authors: Michael H. Freedman and Zheng-Xu He
Journal: Proc. Amer. Math. Soc. 104 (1988), 1305-1310
MSC: Primary 57R50; Secondary 58F99
MathSciNet review: 937012
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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 [Enhancements On Off] (What's this?)

  • [D] A. Denjoy, Sur les courbes définies par les équations différentielles à la surface du tore, J. Math. Pures Appl. 11 (1932), 333-375.
  • [H1] J. Harrison, Unsmoothable diffeomorphisms, Ann. of Math. 102 (1975), 85-94. MR 0388458 (52:9294)
  • [H2] -, Unsmoothable diffeomorphisms on higher dimensional manifolds, Proc. Amer. Math. Soc. 73 (1979), 249-255. MR 516473 (80g:57045)

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Article copyright: © Copyright 1988 American Mathematical Society

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