can someone provide explicit charts for non-standard differentiable structures on, for instance $\mathbb{R}^4$ (or some other manifold)?
explicit "exotic" charts
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differential-topology
low-dimensional-topology
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0I'm a little confused by the nature of your question. Are you interested in simple examples of smooth manifolds with "non-standard" differentiable structures, or are you interested in clutching constructions with charts? I don't see how the Brieskorn example satisfies your original question -- neither Brieskorn nor Kervaire-Milnor provided explicit chart constructions for such manifolds. What are you looking for, precisely? – 2011-03-29
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1i wanted explicit charts (if any are known). i added the other part to maybe drum up interest in the question or to expand it to include constructions (since no one had written anything). – 2011-03-30