Can you exhibit an example of a noncontractible domain in R^n with the dth cohomology groups trivial for all d greater or equal to 1? Thank you
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closed as off topic by Anthony Quas, David White, Oscar RandalWilliams, Todd Trimble♦, Steven Landsburg Nov 13 '12 at 17:11Questions on MathOverflow are expected to relate to research level mathematics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here. If this question can be reworded to fit the rules in the help center, please edit the question. 


There are a million examples. You should google "acyclic space". Here is one: if you remove a point from a homology sphere you get a manifold whose cohomology is trivial in positive degrees. Take a tubular neighbourhood of it in some $\mathbf R^n$ and you get an open domain. 

