I am entirely new to this topic of inquiry and my background in algebraic/topology is fragile. However, I came upon a question I don't have an answer to.
Given any natural number $n$, is there a known example of a bounded (if not, then unbounded) domain (an open connected set) $\mathcal D$ in $\mathbb{R}^{2n}$ such that the boundary $\partial \mathcal D$ consists of $n$ submanifolds of dimensions $1,3,5,\ldots,2n-1$?
If an explicit example is not known, then how can one create one? It will be very helpful if one points me in the direction that will help to create such a domain. I am willing to take a course on a topic if it is required.
Thank you.