I looked on the site but I did not find anything matching my problem.
I am working in 4D with cubical complexes, also known as Khalimsky grids; I mean that I work with "cubical" manifolds.
Do you know if it is possible that, starting from two topological 4-manifolds A and B, the union of A and B is a 4-manifold too, even if the intersection of A and B is the union of two 3D cubes which share a vertex, that is, even if the shared space between the two manifolds is not a 3-manifold ?
I heard about "connected sums" of manifolds which preserve manifoldness, however the intersection of my two manifolds here is not a manifold itself.
Thank you in advance guys, I would really appreciate your help.