Can you exhibit an example of a noncontractible domain in R^n with the d-th cohomology groups trivial for all d greater or equal to 1?
Thank you



Noncontractible domain with trivial cohomology
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.


