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Is there any interest among mathematicians in the topological and geometric properties of nowhere differentiable manifolds? I have seen many mentions of non-differentiable functions of a real variable in topology texts like the Weierstrass P-function for example.

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 What does the term "nowhere differentiable manifold" mean? – Ryan Budney Aug 19 2011 at 18:48
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 Ryan, maybe a topological manifold that has no differentiable structure on it? So the transition functions are homeomorphisms but cannot be refined into either bilipschitz maps or $C^1$ diffeomorphisms? There is even an intermediate category of quasiconformal manifolds studied by Donaldson and Sullivan. – Deane Yang Aug 19 2011 at 19:05
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 I suspect what the OP is after might be extracted from any discussion of the difference between topological and differentiable manifolds. See e.g. en.wikipedia.org/wiki/… though wikipedia seems not to be working for me at the moment. – jc Aug 19 2011 at 19:12
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 A topological manifold without a differentiable structure nevertheless has large parts that admit differentiable structures. So it's not clear how "*nowhere* differentiable" could refer to these. – Andreas Blass Aug 19 2011 at 21:22
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 There may well be the germ of a worthwhile question here, but I think the author needs to put more effort into reformulating the question more precisely (see the comments of quid and Andreas Blass). Voting to close the question, in its present form – Yemon Choi Aug 19 2011 at 21:50
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closed as not a real question by Ryan Budney, Yemon Choi, Andrew Stacey, S. Carnahan♦ Aug 20 2011 at 9:19

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