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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
DOI: https://doi.org/10.1090/S0002-9939-1988-0937012-X
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.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0937012-X
Article copyright: © Copyright 1988 American Mathematical Society