This is a follow-up to my earlier [question][1].

Let $\Sigma\subset \mathbb{S}^{n}$ be a hypersurface -- here $\mathbb{S}^{n}$ is a smooth sphere (possibly exotic ... if this makes a difference).  If $\Sigma$ is a homology sphere, then is it possible for the components of $\mathbb{S}^{n+1}\backslash \Sigma$ to be non-contractible?  





  [1]: https://mathoverflow.net/questions/209761/topology-of-hypersurface-of-sphere-fixed-by-homeomorphic-involution